Archimedes number

The Archimedes number is generally used in design of tubular chemical process reactors. The following are non-exhaustive examples of using the Archimedes number in reactor design.

The Archimedes number is applied often in the engineering of packed beds, which are very common in the chemical processing industry.{{Cite book|title=Chemical Reactor Design, Optimization, and Scaleup|last=Nauman|first=E. Bruce|publisher=John Wiley & Sons|year=2008|edition=2nd|pages=324}} A packed bed reactor, which is similar to the ideal plug flow reactor model, involves packing a tubular reactor with a solid catalyst, then passing incompressible or compressible fluids through the solid bed. When the solid particles are small, they may be "fluidized", so that they act as if they were a fluid. When fluidizing a packed bed, the pressure of the working fluid is increased until the pressure drop between the bottom of the bed (where fluid enters) and the top of the bed (where fluid leaves) is equal to the weight of the packed solids. At this point, the velocity of the fluid is just not enough to achieve fluidization, and extra pressure is required to overcome the friction of particles with each other and the wall of the reactor, allowing fluidization to occur. This gives a minimum fluidization velocity, $u\_\{mf\}$, that may be estimated by:{{Cite book|title=Multiphase Catalytic Reactors - Theory, Design, Manufacturing, and Applications|last1=Önsan|first1=Zeynep Ilsen|last2=Avci|first2=Ahmet Kerim|publisher=John Wiley & Sons|year=2016|pages=83}}

:$u\_\{mf\}=\backslash frac\{\backslash mu\}\{\backslash rho\_ld\_v\}\backslash left((33.7^2+0.0408\backslash text\{Ar\})^\backslash frac\{1\}\{2\}-33.7\backslash right)$

where:

• $d\_v$ is the diameter of sphere with the same volume as the solid particle and can often be estimated as $d\_v\backslash approx\; 1.13d\_p$, where $d\_p$ is the diameter of the particle.

Another use is in the estimation of gas holdup in a bubble column. In a bubble column, the gas holdup (fraction of a bubble column that is gas at a given time) can be estimated by:{{Cite journal|last1=Feng|first1=Dan|last2=Ferrasse|first2=Jean-Henry|last3=Soric|first3=Audrey|last4=Boutin|first4=Olivier|date=April 2019|title=Bubble characterization and gas–liquid interfacial area in two phase gas–liquid system in bubble column at low Reynolds number and high temperature and pressure|journal=Chem Eng Res Des|volume=144|pages=95–106|doi=10.1016/j.cherd.2019.02.001 |s2cid=104422302 |doi-access=free|bibcode=2019CERD..144...95F }}

:$\backslash varepsilon\_g=b\_1\backslash left[\backslash text\{Eo\}^\{b2\}\backslash text\{Ar\}^\{b3\}\backslash text\{Fr\}^\{b4\}\backslash left(\backslash frac\{d\_r\}\{D\}\backslash right)^\{b5\}\backslash right]^\{b6\}$

where:

• $\backslash varepsilon\_g$ is the gas holdup fraction
• $\backslash text\{Eo\}$ is the Eötvos number
• $\backslash text\{Fr\}$ is the Froude number
• $d\_r$ is the diameter of holes in the column's spargers (holed discs that emit bubbles)
• $D$ is the column diameter
• Parameters $b1$ to $b6$ are found empirically

A spouted bed is used in drying and coating. It involves spraying a liquid into a bed packed with the solid to be coated. A fluidizing gas fed from the bottom of the bed causes a spout, which causes the solids to circle linearly around the liquid.{{Cite book|title=Fluidization, Solids Handling, and Processing - Industrial Applications|last=Yang|first=W-C|publisher=William Andrew Publishing/Noyes|year=1998|pages=335}} Work has been undertaken to model the minimum velocity of gas required for spouting in a spouted bed, including the use of artificial neural networks. Testing with such models found that Archimedes number is a parameter that has a very large effect on the minimum spouting velocity.{{Cite journal|last1=Hosseini|first1=SH|last2=Rezaei|first2=MJ|last3=Bag-Mohammadi|first3=M|last4=Altzibar|first4=H|last5=Olazar|first5=M|date=October 2018|title=Smart models to predict the minimum spouting velocity of conical spouted beds with non-porous draft tube|journal=Chem Eng Res Des|volume=138|pages=331–340|doi=10.1016/j.cherd.2018.08.034 |bibcode=2018CERD..138..331H |s2cid=105461210 }}

• Viscous fluid dynamics
• Convection
• Convection (heat transfer)
• Dimensionless quantity
• Galilei number
• Grashof number
• Reynolds number
• Froude number
• Eötvös number
• Sherwood number

{{NonDimFluMech}}

{{DEFAULTSORT:Archimedes Number}}

Category:Dimensionless numbers of fluid mechanics

Category:Fluid dynamics