X-Virus-Scanned: clean according to Sophos on Logan.com X-SpamCatcher-Score: 41 [XX] Return-Path: Received: from ms-smtp-01.southeast.rr.com ([24.25.9.100] verified) by logan.com (CommuniGate Pro SMTP 5.1.8) with ESMTP id 2021848 for flyrotary@lancaironline.net; Wed, 02 May 2007 13:34:24 -0400 Received-SPF: pass receiver=logan.com; client-ip=24.25.9.100; envelope-from=eanderson@carolina.rr.com Received: from edward2 (cpe-024-074-103-061.carolina.res.rr.com [24.74.103.61]) by ms-smtp-01.southeast.rr.com (8.13.6/8.13.6) with SMTP id l42HX8ms020267 for ; Wed, 2 May 2007 13:33:09 -0400 (EDT) Message-ID: <000301c78ce0$1ff19f00$2402a8c0@edward2> From: "Ed Anderson" To: "Rotary motors in aircraft" Subject: Source Material - Boundary layer with pressure gradient.htm Date: Wed, 2 May 2007 13:34:21 -0400 MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_NextPart_000_0003_01C78CBE.978FD850" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.3028 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3028 X-Virus-Scanned: Symantec AntiVirus Scan Engine This is a multi-part message in MIME format. ------=_NextPart_000_0003_01C78CBE.978FD850 Content-Type: multipart/alternative; boundary="----=_NextPart_001_0004_01C78CBE.978FD850" ------=_NextPart_001_0004_01C78CBE.978FD850 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Only for those who (Dave? Bill?, Rusty?.....) wish to punish themselves = with more minutia on air flow in ducts/diffusers. A month or two ago, I posted some slides extracted from a university = study/course on the effects of airflow separation inside a duct. This = involved the boundary layer which appears to act somewhat different = inside the constraining walls of a duct as compared to its free flow = across an airfoil. The cause of flow separation in the duct being the = pressure build up by the expansion in duct area which led to two = counteracting forces.=20 The pressure build up actually helps the boundary layer stay attached to = curving duct wall - for a time. But, this same pressure that helps = "push" the boundary layer against the duct wall also slows down the = boundary layer which ultimately leads to flow separation and reversal.=20 This "understanding" led me to my "pinched duct" design to accelerate = the boundary layer and cause it to penetrate further into the higher = pressure area before separation. I also inferred that this effect was = what made the Streamline duct of K&W so effective. No claim was made = that the pinched ducts were anywhere nearly as effective as the = Streamline duct, but were an attempt to meet a space constraint. Most attempts to use the streamline duct in a space too small involves = truncating the duct from the inlet end. However, while this does tend = to preserve some of its effectiveness, if the distance is very short = (like my 3 -6 inches) the large expose core area likely increases = cooling drag considerably. So I decided to keep the inlet small (unlike = what truncating the streamline duct would have resulted in) but to pinch = it down to keep the boundary layer velocity high resulting (hopefully) = in further penetration down the duct before flow separation occurred. Some questioned my interpretation (always a smart thing to do, as I = only had one short course in aerodynamics as an Electrical Engineering = student - so my attention was probably not as keenly focused as it = should have been {:>)). In any case, I went looking for the source = document so that any interested could read it and draw their own = conclusion.=20 The original source for this material was = http://www.me.dal.ca/site2/courses/mech3300/5_Separation.ppt. However, = they have (as Universities frequently do) apparently rotated material = presented and removed this briefing from their website. This leaves = the .html portion I saved when first reading the presentation which is = attached. I was only partially successful in providing the source - in that I = found the original script that went with the slide presentation - but = unfortunately the slides are not present with it. I do have a number of = the slides I had previously extracted (used in my presentation) but = since they could be "tainted" by my "explanation" of the slides, I will = not present them. I reviewed the script again and still believe my interpretation is = correct, but others should have the opportunity to decide for = themselves. We do that sort of thing on this list. But, if you do decide differently, please don't tell my pinched ducts = {:>) Ed Ed Anderson Rv-6A N494BW Rotary Powered Matthews, NC eanderson@carolina.rr.com http://members.cox.net/rogersda/rotary/configs.htm#N494BW http://www.dmack.net/mazda/index.html ------=_NextPart_001_0004_01C78CBE.978FD850 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Only for those who (Dave? Bill?, Rusty?.....) = wish to=20 punish themselves with more minutia on air flow in = ducts/diffusers.
 
A month or two ago, I posted some slides = extracted from a=20 university study/course on the effects of airflow separation inside a=20 duct. This involved the boundary layer which appears to act = somewhat=20 different inside the constraining walls of a duct as compared to = its free=20 flow across an airfoil.   The cause of flow separation in the = duct=20  being the pressure build up by the expansion in duct area = which led=20 to two counteracting forces. 
 
The pressure build up actually helps the = boundary layer=20 stay attached to curving duct wall - for a time.  = But,=20 this same pressure that helps "push" the boundary layer against the duct = wall=20 also slows down the boundary layer which ultimately leads to flow=20 separation and reversal. 
 
 This "understanding" led me to my "pinched = duct"=20 design to accelerate the boundary layer and cause it to penetrate = further into=20 the higher pressure area before separation.  I also inferred that=20 this effect  was what made the Streamline duct of K&W so=20 effective.  No claim was made that the pinched ducts were anywhere = nearly=20 as effective as the Streamline duct, but were an attempt to meet a space = constraint.
 
Most attempts to use the streamline duct in a space too small = involves=20 truncating the duct from the inlet end.  However, while this does = tend to=20 preserve some of its effectiveness, if the distance is very short (like = my 3 -6=20 inches) the large expose core area likely increases cooling drag=20 considerably.  So I decided to keep the inlet small (unlike what = truncating=20 the streamline duct would have resulted in) but to pinch it down to keep = the=20 boundary layer velocity high resulting (hopefully) in further = penetration down=20 the duct before flow separation occurred.
 
Some questioned my interpretation (always a = smart thing to=20 do,  as I only had one short course in aerodynamics as an = Electrical=20 Engineering  student - so my attention was probably not as keenly=20 focused as it should have been {:>)).  In any case,  I = went=20 looking for the source document so that any interested could read it and = draw=20 their own conclusion. 
 
  The original source for this material was = http://www.me.dal.ca/site2/courses/mech3300/5_Separation.ppt.  However, they have (as = Universities=20 frequently do) apparently rotated material presented and removed this=20  briefing from their website.  This leaves the .html portion I = saved=20 when first reading the presentation which is = attached.
 
I was only partially successful in providing the = source=20  - in that I found the original script that went with the = slide=20 presentation - but unfortunately the slides are not present with = it.  I do=20 have a number of the slides I had previously extracted (used in my = presentation)=20 but since they could be "tainted" by my "explanation" of the slides, I = will not=20 present them.
 
I reviewed the script again and still believe my interpretation is = correct,=20 but others should have the opportunity to decide for themselves. We = do that=20 sort of thing on this list.
 
 
 But, if you do decide differently, please don't tell my = pinched ducts=20 {:>)
 
 
 
Ed
Ed Anderson
Rv-6A N494BW Rotary Powered
Matthews, NC
eanderson@carolina.rr.comhttp:/= /members.cox.net/rogersda/rotary/configs.htm#N494BW
http://www.dmack.net/mazda= /index.html
 
  ------=_NextPart_001_0004_01C78CBE.978FD850-- ------=_NextPart_000_0003_01C78CBE.978FD850 Content-Type: text/html; name="Boundary layer with pressure gradient.htm" Content-Transfer-Encoding: quoted-printable Content-Disposition: attachment; filename="Boundary layer with pressure gradient.htm" =EF=BB=BF Boundary layer with pressure gradient
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Boundary layer = with pressure=20 gradient in flow=20 direction.  

Separation & = Flow induced=20 Vibration

Unit # 5: = Potter 8.6.7, 8.2,=20 8.3.2

 

Boundary layer = flow with pressure = gradient 

So far we neglected the = pressure=20 variation along the flow=20 in a boundary layer

This is not = valid for=20 boundary layer over curved surface like airfoil

Owing to object=E2=80=99s = shape the free stream=20 velocity just outside the boundary layer varies along the length of the=20 surface.

As per = Bernoullis equation,=20 the static pressure on the surface of the object, therefore, varies in = x-=20 direction along the surface.

There is no = pressure=20 variation in the y- direction within the boundary layer. Hence pressure in = boundary layer is=20 equal to that just outside it.

As this = pressure just=20 outside of a boundary layer varies along x axis that inside the boundary = layer=20 also varies along x axis

 

Separation 

In a situation where pressure increases = down stream=20 the fluid particles can move up against it  by virtue of its = kinetic=20 energy. 

Inside the boundary layer = the velocity=20 in a layer could reduce so much that the kinetic energy of the fluid = particles=20 is no longer adequate to move the particles against the pressure=20 gradient. 

This leads to flow=20 reversal. 

Since the fluid layer = higher up still=20 have energy to mover forward a rolling of fluid streams occurs, which is = called=20 separation=20

 

Onset of separation 

Click to add = text

 

Figure 8.27 =E2=80=93 = Influence of a strong=20 pressure gradient on a turbulent flow: (a) a strong = negative=20 pressure gradient may re-laminarize a flow; (b) a strong = positive=20 pressure gradient causes a strong boundary layer top thicken.  = (Photograph=20 by R.E. Falco)

 

Bernoullis=20 equation 

It is valid just outside Boundary Layer, = where=20 between two points (1,2) on the flow = stream


       (1) 
 = ;=20  
Since = pressure in the=20 boundary layer is same on y axis and that just outside, the expression = for=20 pressure gradient along x is also valid inside the boundary = layer.

Navier Stokes eq. is valid inside = boundary layer. Eq.=20 (8.6.45) from Potter we=20 have 
        =20 (2)

 

Substituting in Eq. (2) = boundary=20 condition at wall u=3D0, v=3D0 we=20 get 
 
 
      &nbs= p; (3) =20

It is valid for both laminar = &=20 turbulent flows as very near the wall both flows are laminar

From the = above expression=20 we see that when pressure decreases second derivative of velocity is = negative.=20 So the velocity initially increases fast and then gently blend with the = free=20 stream velocity U

For adverse pressure gradient = ( dP/dx=20 >0) second derivative is positive at wall but must be negative at the = top of=20 boundary layer to match with U. Thus it must pass through a point of=20 inflexion.

Separation occurs = when the=20 velocity gradient is zero at the wall and shear stress at wall is=20 zero

 

Influence of the pressure = gradient.=20

 

Separation=20  

Separation starts = with zero=20 velocity gradient at the wall  

Flow reversal = takes place=20 beyond separation=20 point 
dP/dx = >0

Adverse pressure gradient is = necessary=20 for separation 

There is no pressure = change after separation So, = pressure in=20 the separated region is constant.

Fluid in turbulent boundary = layer has=20 appreciably more momentum than the flow of a laminar = B.L. Thus=20 a turbulent B.L can penetrate further into an adverse pressure gradient = without=20 separation

 

Smooth = ball   Rough=20 ball

 

Effect of a = wire ring on separation

 

Effect of separation 

There is an increase in drag = as a result=20 of separation = as it=20 prevents pressure recovery

There is low = pressure in=20 separated region and it persists in the entire region.

Turbulent eddies formed due = to separation can not = convert=20 their rotational energy back into pressure head. So there is no pressure = recovery (increase).  The difference between high pressure at the = front and=20 low pressure at rear increases the drag.

This increase = in drag=20 overshadows any increase in lift due to increase in the angle of=20 attack

 

Control of separation 

Streamlining reduces adverse = pressure=20 gradient beyond the maximum thickness and delays separation

Fluid particles lose kinetic = energy near=20 separation = point. So=20 these are either removed by suction or higher energy=20  
 
 

High energy fluid is blown = near separation = point

Roughening surface to force = early=20 transition to turbulent boundary layer

 

Separation delays = by=20 suction 

Click to add = text

 

Pressure & = Velocity=20 change in a converging diverging duct

 

Boundary layer = growth in a=20 nozzle-diffuser 

Area

Increasing 

Area

Constant=20  

Area

Decreasing 

Pressure = gradient

Adverse 

Pressure = gradient

Zero 

Pressure = gradient

Favourable 

Pressure = increases 

Pressure = Constant =  

Pressure = decreases 

Velocity

decreasing 

Velocity = Constant =  

Velocity

increasing 

Diffuser 

Throat 

Nozzle

 

Problem=20 (White-7.63) 

Assume that the front surface = velocity on=20 an infinitely long cylinder is given by potential theory , V =3D=20 2Usinq from which the surface pressure is computed by Bernoullis = equation. In=20 the separated flow on the=20 rear, the pressure is assumed equal to its value at  q=3D90. Compute the=20 theoretical drag coefficient and compare that with the  = experimental value=20 of 1.2 
[This = problem may=20 show the inadequacy of potential flow theory near the=20 surface]

 

Flow induced=20 vibration 
(Von Karman Vortex) 

Vortices are created on both = sides of a=20 symmetric blunt object.

However the = vortices are=20 not created simultaneously on both ends. So this leads to alternate = shedding of=20 vortices in the flow=20 range 40<Re<10,000.

This induces a vibration, = which if=20 matched with the natural frequency of the object may be = disastrous.

The frequency f is related to Strouhl number St = =3D fD/U,=20 where D is diameter and U is velocity. St =3D 0.198(1-19.7/Re) for=20 250<Re<2x105

 

Home work = (Potter=20 p-361) 

The velocity of a slow moving = air=20 (kinematic viscosity=3D1.6x10-5) is to be measured using a  6 cm = cylinder.=20 The velocity range expected to be 0.1<U <1 m/s. Do you expect = vortex=20 shedding to occur?

If so, what frequency would = be observed=20 by the pressure measuring device for U=3D1 m/s.

 

Drag on=20 airfoil 

Separation is = reduced by=20 slightly bending the leading edge.

By giving air = foil shape to=20 the plate drag is further reduced

But further tilting brings = back the separation

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