FBR Fluid Mechanics

<BODY BGCOLOR="#FFFFFF" TEXT="#000000" LINK="#0000FF" VLINK="FF0000" ALINK="FF0000" BACKGROUND="../../Backgrounds/blueston.jpg"><A NAME="buttons"><CENTER><A HREF="../index.htm#index" TARGET="_parent"><IMG SRC="../Images/index.gif"></A><A HREF="packed_beds_scroll.htm" TARGET="_parent"><IMG SRC="../Images/left.gif"></A><A HREF="../FBR_Solve/solve_intro_scroll.htm" TARGET="_parent"><IMG SRC="../Images/right.gif"></A><A HREF="mailto:finlayson@cheme.washington.edu""><IMG SRC="../Images/mail.gif"></A></CENTER><P><HR><A NAME="top"><P><H2>Fluid Mechanics for Fluidized Beds</H2><HR><P>To better understand fluidization of a particle bed, it is necessary to determine what range of flow rates allow fluidization, and also, what flow rates will begin to carry the particles out the top of the particle chamber. We wish to determine a minimum flow rate allowing the particles to become fluidized, the minimum fluidization velocity (um), and the flow rate which carries the first particle out of the chamber, the terminal velocity (ut).<P>We used the <B><EM>Ergun equation</B></EM> on the <A HREF="packed_beds_scroll.htm#ergun" TARGET=_parent>packed bed page</A> to describe the drag exerted on a particle bed by the fluid flow. By setting this equation equal to the gravitational force of the particle bed, we can determine the minimum fluidization velocity (um). In this case, the equation is rearranged:<P><IMG SRC="../Images/ergun2.gif" ALIGN=MIDDLE><IMG SRC="../Images/erg_def2.gif" HSPACE=20 VSPACE=20 ALIGN=TOP><P>The above equation is a quadratic in u, where u now stands for um, the minimum fluidization velocity.<HR><P><B>The next step is to determine ut.</B><P>The ut is the velocity that is large enough to lift a single particle and carry it out of the fluidized bed. Then the equations are those for drag past a sphere. There are three equations for the drag coefficient corresponding to the three flow regimes:<P><UL><B><LI>laminar, where Re < 1 ,<LI>transition from laminar to turbulent, where 1 < Re < 500 and<LI>turbulent, where 500 < Re < 200,000.</B></UL><P>This implies there are three different equations for ut corresponding to these flow regimes. The image below contains the ut equations for the three flow regimes.<P><P><CENTER><IMG SRC="../Images/re_ut.gif"></CENTER> <HR> <P><H3>Fluidized Bed Animations</H3> The plot below represents the Ergun equation (the first equation shown above), where the left hand side of the equation is the pressure drop.<B>Click on the curve to see the effects of increased gas velocity on particle movement.</B> <P><CENTER><A HREF="/cgi-bin/imagemap/~dt/FBR_Pages/Imagemaps/fbr_plt.map"> <IMG SRC="../Imagemaps/fbr_plt.jpg" ISMAP></A></CENTER> <A NAME="Imagemap"><P Align="Center"><HR Size=3></P> <ADDRESS><B>Doug Thornhill</B></ADDRESS> <A NAME="address"></BODY>