Dimensionless Velocity For Fluidized Reactors At G/S Contacting Regime Calculator

Dimensionless Velocity Formula:

\[ u' = u \times \left( \frac{\rho_{gas}^2}{\mu_L \times (\rho_{solids} - \rho_{gas}) \times g} \right)^{1/3} \]

Velocity in Tube:

m/s

Density of Gas:

kg/m³

Viscosity of Liquid:

Pa·s

Density of Solids:

kg/m³

Dimensionless Velocity (u'):

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1. What is Dimensionless Velocity?

Dimensionless velocity is a parameter used to characterize the flow behavior of the gas phase relative to the solid particles within fluidized reactors at gas-solid contacting regime. It provides a normalized measure of velocity that accounts for various fluid and particle properties.

2. How Does the Calculator Work?

The calculator uses the dimensionless velocity formula:

\[ u' = u \times \left( \frac{\rho_{gas}^2}{\mu_L \times (\rho_{solids} - \rho_{gas}) \times g} \right)^{1/3} \]

Where:

\( u' \) — Dimensionless velocity
\( u \) — Velocity in tube (m/s)
\( \rho_{gas} \) — Density of gas (kg/m³)
\( \mu_L \) — Viscosity of liquid (Pa·s)
\( \rho_{solids} \) — Density of solids (kg/m³)
\( g \) — Gravitational acceleration (9.80665 m/s²)

Explanation: The formula normalizes the actual velocity by considering the relative densities of gas and solids, liquid viscosity, and gravitational effects to provide a dimensionless parameter for flow characterization.

3. Importance of Dimensionless Velocity Calculation

Details: Dimensionless velocity is crucial for analyzing fluidized bed reactors, predicting flow regimes, optimizing reactor design, and understanding the interaction between gas and solid phases in various industrial processes.

4. Using the Calculator

Tips: Enter velocity in m/s, densities in kg/m³, and viscosity in Pa·s. All values must be positive numbers. The calculator will compute the dimensionless velocity which characterizes the flow behavior in fluidized reactors.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of dimensionless velocity in fluidized reactors?
A: Dimensionless velocity helps characterize the flow regime, predict particle behavior, and optimize reactor performance by providing a normalized measure of gas velocity relative to solid particles.

Q2: What are typical ranges for dimensionless velocity?
A: The range varies depending on the specific application, but typically values between 0.01-10 are encountered in different flow regimes of fluidized bed reactors.

Q3: How does density difference affect dimensionless velocity?
A: A larger density difference between solids and gas generally results in a lower dimensionless velocity for the same actual velocity, indicating different flow characteristics.

Q4: What are the limitations of this calculation?
A: The formula assumes ideal conditions and may need adjustments for non-spherical particles, polydisperse systems, or complex fluid properties in real industrial applications.

Q5: Can this be used for different fluidized bed configurations?
A: While the basic principle applies, specific reactor geometries and operating conditions may require additional considerations or modified correlations.