Flow separation

<h2 id="adverse-pressure-gradient">Adverse pressure gradient</h2>

<p>The flow reversal is primarily caused by <a href="/facts/Adverse_pressure_gradient/PXBuvTUJ">adverse pressure gradient</a> imposed on the boundary layer by the outer <a href="/facts/Potential_flow/chXFn3Cw">potential flow</a>. The streamwise momentum equation inside the boundary layer is approximately stated as
</p>

u
        
          
            
              ∂
              u
            
            
              ∂
              s
            
          
        
        =
        −
        
          
            1
            ρ
          
        
        
          
            
              d
              p
            
            
              d
              s
            
          
        
        +
        
          ν
        
        
          
            
              
                ∂
                
                  2
                
              
              u
            
            
              ∂
              
                y
                
                  2
                
              
            
          
        
      
    
    {\displaystyle u{\partial u \over \partial s}=-{1 \over \rho }{dp \over ds}+{\nu }{\partial ^{2}u \over \partial y^{2}}}

<p>where 
  
    
      
        s
        ,
        y
      
    
    {\displaystyle s,y}
  
 are streamwise and normal coordinates.
An adverse pressure gradient is when 
  
    
      
        d
        p
        
          /
        
        d
        s
        >
        0
      
    
    {\displaystyle dp/ds>0}
  
, which then can be seen to cause the velocity 
  
    
      
        u
      
    
    {\displaystyle u}
  
 to decrease along 
  
    
      
        s
      
    
    {\displaystyle s}
  
 and possibly go to zero if the adverse pressure gradient is strong enough.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p>
<h2 id="influencing-parameters">Influencing parameters</h2>
<p>The tendency of a boundary layer to separate primarily depends on the distribution of the adverse or negative
edge velocity gradient 
  
    
      
        d
        
          u
          
            o
          
        
        
          /
        
        d
        s
        (
        s
        )
        <
        0
      
    
    {\displaystyle du_{o}/ds(s)<0}
  
 along the surface, which in turn is directly related to the pressure and its gradient by the differential form of the <a href="/facts/Bernoulli_principle/Y7urHvPr">Bernoulli relation</a>,
which is the same as the momentum equation for the outer inviscid flow.
</p>

ρ
        
          u
          
            o
          
        
        
          
            
              d
              
                u
                
                  o
                
              
            
            
              d
              s
            
          
        
        =
        −
        
          
            
              d
              p
            
            
              d
              s
            
          
        
      
    
    {\displaystyle \rho u_{o}{du_{o} \over ds}=-{dp \over ds}}

<p>But the general magnitudes of 
  
    
      
        d
        
          u
          
            o
          
        
        
          /
        
        d
        s
      
    
    {\displaystyle du_{o}/ds}
  
 required for separation are much greater for <a href="/facts/Turbulence/NpgFUhG5">turbulent</a> than for <a href="/facts/Laminar_flow/RFXN4eAC">laminar</a> flow, the former being able to tolerate nearly an order of magnitude stronger flow deceleration. A secondary influence is the <a href="/facts/Reynolds_number/4sdungsf">Reynolds number</a>. For a given adverse 
  
    
      
        d
        
          u
          
            o
          
        
        
          /
        
        d
        s
      
    
    {\displaystyle du_{o}/ds}
  
 distribution, the separation resistance of a turbulent boundary layer increases slightly with increasing Reynolds number. In contrast, the separation resistance of a laminar boundary layer is independent of Reynolds number — a somewhat counterintuitive fact.
</p>
<h2 id="internal-separation">Internal separation</h2>

<p>Boundary layer separation can occur for internal flows. It can result from such causes such as a rapidly expanding duct of pipe. Separation occurs due to an adverse pressure gradient encountered as the flow expands, causing an extended region of separated flow. The part of the flow that separates the recirculating flow and the flow through the central region of the duct is called the dividing streamline.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> The point where the dividing streamline attaches to the wall again is called the reattachment point. As the flow goes farther downstream it eventually achieves an equilibrium state and has no reverse flow.
</p>
<h2 id="effects-of-boundary-layer-separation">Effects of boundary layer separation</h2>
<p>When the boundary layer separates, its remnants form a shear layer<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> and the presence of a separated flow region between the shear layer and surface modifies the outside <a href="/facts/Potential_flow/chXFn3Cw">potential flow</a> and pressure field. In the case of airfoils, the pressure field modification results in an increase in <a href="/facts/Pressure_drag/1FVstxos">pressure drag</a>, and if severe enough will also result in  <a href="/facts/Stall_(flight)/nsB7YRc5">stall</a> and loss of lift, all of which are undesirable. For internal flows, flow separation produces an increase in the flow losses, and stall-type phenomena such as <a href="/facts/Compressor_stall/1JeWULC7">compressor surge</a>, both undesirable phenomena.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a>
</p><p>Another effect of boundary layer separation is regular shedding vortices, known as a <a href="/facts/K%25C3%25A1rm%25C3%25A1n_vortex_street/67b7qb3v">Kármán vortex street</a>. Vortices shed from the bluff downstream surface of a structure at a frequency depending on the speed of the flow. Vortex shedding produces an alternating force which can lead to vibrations in the structure. If the shedding frequency coincides with a <a href="/facts/Resonance_frequency/q7VLALUz">resonance frequency</a> of the structure, it can cause structural failure. These vibrations could be established and reflected at different frequencies based on their origin in adjacent solid or fluid bodies and could either damp or amplify the resonance.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Triple-deck_theory/vSSAS5ct">Triple-deck theory</a></li>
<li><a href="/facts/Aerodynamics/Cn6Lnl3H">Aerodynamics</a></li>
<li><a href="/facts/D%2527Alembert%2527s_paradox/zHRDuy9J">D'Alembert's paradox</a></li>
<li><a href="/facts/Magnus_effect/Sgolud8d">Magnus effect</a></li></ul>
<h2 id="footnotes">Footnotes</h2>

<ul><li>Anderson, John D. (2004), <i>Introduction to Flight</i>, McGraw-Hill. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-07-282569-3.</li>
<li><a href="/facts/L._J._Clancy/6xTu8Llt">L. J. Clancy</a> (1975), <i>Aerodynamics</i>, Pitman Publishing Limited, London <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-273-01120-0.</li></ul>
<h2 id="external-links">External links</h2>

Wikimedia Commons has media related to Flow separation.

<ul><li><a href="http://www.aerospaceweb.org/question/aerodynamics/q0215.shtml"><i>Aerospaceweb</i>-Golf Ball Dimples & Drag</a></li>
<li><a href="https://web.archive.org/web/20070616051443/http://www.fi.edu/wright/again/wings.avkids.com/wings.avkids.com/Book/Sports/instructor/golf-01.html">Aerodynamics in Sports Equipment, Recreation and Machines – Golf – Instructor</a></li>
<li><a href="http://www.anade-itn.eu/">Marie Curie Network on Advances in Numerical and Analytical Tools for Detached Flow Prediction</a> <a href="https://web.archive.org/web/20181102065251/http://www.anade-itn.eu/">Archived</a> 2 November 2018 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>White (2010), "Fluid Mechanics", Section 7.1 (7th edition) <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Anderson, John D. (2004), Introduction to Flight, Section 4.20 (5th edition) <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>L. J. Clancy (1975) Aerodynamics, Section 4.14 <a href="/wiki/L._J._Clancy" target="_blank">/wiki/L._J._Clancy</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Fundamentals of Aerodynamics 5th edition, John D. Anderson, Jr. 2011, ISBN 978 0 07 339810 5, Figure 4.46 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Balmer, David (2003) Separation of Boundary Layers Archived 17 July 2020 at the Wayback Machine, from School of Engineering and Electronics,  University of Edinburgh <a href="http://www.homepages.ed.ac.uk/johnc/teaching/fluidmechanics4/2003-04/fluids14/separation.html" target="_blank">http://www.homepages.ed.ac.uk/johnc/teaching/fluidmechanics4/2003-04/fluids14/separation.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Wilcox, David C. Basic Fluid Mechanics. 3rd ed. Mill Valley: DCW Industries, Inc., 2007. 664-668. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>https://www.aps.org/units/dfd/resources/upload/prandtl_vol58no12p42_48.pdf, Fig 3 <a href="https://www.aps.org/units/dfd/resources/upload/prandtl_vol58no12p42_48.pdf" target="_blank">https://www.aps.org/units/dfd/resources/upload/prandtl_vol58no12p42_48.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Fielding, Suzanne. "Laminar Boundary Layer Separation." 27 October 2005. The University of Manchester. 12 March 2008 <https://community.dur.ac.uk/suzanne.fielding/teaching/BLT/sec4c.pdf>. <a href="https://community.dur.ac.uk/suzanne.fielding/teaching/BLT/sec4c.pdf" target="_blank">https://community.dur.ac.uk/suzanne.fielding/teaching/BLT/sec4c.pdf</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
</ol>

Flow separation open-in-new

Flow separation