<span style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;">현재 간단한 0.012mm (diameter) 에 0.5m (length) 파이프에 25 Celsius degrees, no slip condition at 1 atm, Uo = 0.4m/s, No heat transfer, No turbulence and Zero gauge static pressure  형태로 air를 inlet에서 outlet으로 내보내는 CFX simulation을 하고있습니다. (사진 참조)<br></span><br><div style="text-align:left;"><img src="http://thimg.todayhumor.co.kr/upfile/201502/14235337048kZeWzmRcJD7rN9BlEd.png" width="800" height="477" alt="Capture - Copy.PNG" class="chimg_photo" style="border:none;"></div> <div style="text-align:left;"><img src="http://thimg.todayhumor.co.kr/upfile/201502/1423533709Djo24S1HH1rmmA.png" width="800" height="423" alt="cfx 3.PNG" class="chimg_photo" style="border:none;"></div> <div style="text-align:left;"><img src="http://thimg.todayhumor.co.kr/upfile/201502/1423533710OPQwxkO4D8CL4oiqP5GkX1yozK.png" width="800" height="475" alt="cfx6.PNG" class="chimg_photo" style="border:none;"></div><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><span style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;">Fully-developed flow region에서 radial velocity를 찾는다 가정할때 CFX에서 나온 결과값과 </span><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><span style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;">Analytic method : U/Umax = [1-(r/ro)^2]</span><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><p class="MsoNormal" style="margin:0px 0px 0px 20.25pt;color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><span lang="en-us" style="font-size:11pt;line-height:15.6933336257935px;font-family:'Times New Roman', serif;"><br>Where the Umax</span><span lang="en-us" style="font-size:11pt;line-height:15.6933336257935px;font-family:'Times New Roman', serif;"> is the velocity at centerline, r is the radial position and </span><span lang="en-us" style="font-size:10pt;line-height:14.2666664123535px;font-family:'맑은 고딕';"></span><b><span lang="en-us" style="font-family:'Times New Roman', serif;"> </span></b><span lang="en-us" style="font-size:11pt;line-height:15.6933336257935px;font-family:'Times New Roman', serif;">ro is the pipe radius from the centerline. And U is the radial velocity.</span></p><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><span style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"> 의 결과값이 pipe wall에서 현저히 다르게 나오고 centerline 즉 파이프 radius 가 0일때의 radial velocity는 두 결과값이 거의 일치하게 나옵니다.</span><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><br style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;"><span style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;">제가 생각한건 아무리 조건이 no slip condition이라고해도 어디까지나 assumption이고 Nanoscale로 wall을 봤을때는 smooth pipe도 surface friction이 있을거라 생각해봅니다... 혹시 이 두 결과값이 pipe wall에서는 다르게나오지만 centerline에서는 일치하게 나오는 이유를 알고계신분 있을까요?<br><br><br><br><br><br><br><br>------------------추가-----------------<br><br></span> <table border="0" cellpadding="0" cellspacing="0" width="566" style="color:#222222;font-family:arial, sans-serif;font-size:12.8000001907349px;line-height:normal;border-collapse:collapse;width:425pt;"><colgroup><col width="72" style="width:54pt;"><col width="221" style="width:166pt;"><col width="141" style="width:106pt;"><col width="132" style="width:99pt;"></colgroup><tbody><tr height="22" style="height:16.5pt;"><td height="22" width="72" style="margin:0px;height:16.5pt;width:54pt;">Radius from the centerline</td> <td width="221" style="margin:0px;width:166pt;">                                             CFX</td> <td width="141" style="margin:0px;width:106pt;">                      Equation</td> <td width="132" style="margin:0px;width:99pt;">              % Difference</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00021</td> <td align="right" style="margin:0px;">0.63457</td> <td align="right" style="margin:0px;">0.64923</td> <td align="right" style="margin:0px;">-2.31</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00062</td> <td align="right" style="margin:0px;">0.63344</td> <td align="right" style="margin:0px;">0.64304</td> <td align="right" style="margin:0px;">-1.52</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00103</td> <td align="right" style="margin:0px;">0.63190</td> <td align="right" style="margin:0px;">0.63068</td> <td align="right" style="margin:0px;">0.19</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00145</td> <td align="right" style="margin:0px;">0.62735</td> <td align="right" style="margin:0px;">0.61213</td> <td align="right" style="margin:0px;">2.43</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00186</td> <td align="right" style="margin:0px;">0.61647</td> <td align="right" style="margin:0px;">0.58740</td> <td align="right" style="margin:0px;">4.72</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00228</td> <td align="right" style="margin:0px;">0.60536</td> <td align="right" style="margin:0px;">0.55648</td> <td align="right" style="margin:0px;">8.07</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00269</td> <td align="right" style="margin:0px;">0.59393</td> <td align="right" style="margin:0px;">0.51938</td> <td align="right" style="margin:0px;">12.55</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00310</td> <td align="right" style="margin:0px;">0.56932</td> <td align="right" style="margin:0px;">0.47610</td> <td align="right" style="margin:0px;">16.37</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00352</td> <td align="right" style="margin:0px;">0.54007</td> <td align="right" style="margin:0px;">0.42663</td> <td align="right" style="margin:0px;">21.00</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00393</td> <td align="right" style="margin:0px;">0.50639</td> <td align="right" style="margin:0px;">0.37099</td> <td align="right" style="margin:0px;">26.74</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00434</td> <td align="right" style="margin:0px;">0.42262</td> <td align="right" style="margin:0px;">0.30916</td> <td align="right" style="margin:0px;">26.85</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00476</td> <td align="right" style="margin:0px;">0.32510</td> <td align="right" style="margin:0px;">0.24114</td> <td align="right" style="margin:0px;">25.82</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00517</td> <td align="right" style="margin:0px;">0.21881</td> <td align="right" style="margin:0px;">0.16694</td> <td align="right" style="margin:0px;">23.70</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00559</td> <td align="right" style="margin:0px;">0.10321</td> <td align="right" style="margin:0px;">0.08656</td> <td align="right" style="margin:0px;">16.13</td></tr><tr height="22" style="height:16.5pt;"><td height="22" align="right" style="margin:0px;height:16.5pt;">0.00600</td> <td align="right" style="margin:0px;">0.00020</td> <td align="right" style="margin:0px;">0.00000</td> <td align="right" style="margin:0px;">100.06<br><br></td></tr></tbody></table><br>CFD simulation data입니다. 보시다시피 Wall인 r=0.006에서 CFX값은 0.0002고 위 공식에 대입한경우는 0입니다...