Empirical CPMA transfer function

Overview

This web application is created to analyze the transfer function of the CPMA. It utilizes data obtained from tandem CPMA (TCPMA) measurements carried out byNaseri et al. (2023).
To estimate the transfer function and discrepancies of the CPMA, a triangular transfer function was employed. Two factors, namely the width factor (μ) and height factor (𝜂), were utilized to determine any deviations from the idealized triangular transfer function. A value of 1 for each factor indicated that there were no discrepancies between the actual and theoretical triangular CPMA transfer functions.

If the width factor is greater than one (μ>1), it signifies that the CPMA transfer function is narrower than the idealized triangular transfer function.
These two factors are determined through multivariate nonlinear functions that are fitted to TCPMA measurements. The functions take into account either the CPMA mass set point (mp), CPMA resolution (Rm), and CPMA flow rate (Q), or the CPMA rotational speed (ω) and voltage (V). If the CPMA flow rate is set to 0.3, 1.5, 4 or 8 LPM, the loss factor is directly calculated using the fitting function corresponding to the relevant CPMA flow rate. However, for other flow rates, the loss factor is derived through simple interpolation between the nearest lower and higher CPMA flow rates.

Inputs

CPMA dimensions (Cambustion Ltd)

Inner radius r1: 6cm
Outer radius r2: 6.1 cm
Length L: 20 cm
ω2/ω1: 0.9696

Set point mode



Mass set point (mp) fg


m* ∈ [ 0.05 , 100 ] fg

Resolution (Rm)


Rm ∈ [ 2 , 15 ]

flow rate (Q) LPM


Q ∈ [ 0.3 , 8 ] LPM

particle mass fg


mp ∈ [-∞, +∞] fg

Particle properties


Dm
ρeff,100 kg/m3
Charge state z :1
Angular speed ω = - rad/s
ω = - RPM
Voltage V = - V
Mass setpoint m* = -fg
Resolution Rm = -

Results

Under the specified CPMA configuration settings, wherein the width (μ) and height (𝜂) factors of the CPMA transfer function are calculated as below, particles with specified mass exhibit a transmission efficiency of:

Transmission Eff. (ΩCPMA):
-
Height factor (𝜂):
-
Width factor (μ):
-

The diagram below compares the empirical triangular models with the theoretical triangular, trapezoidal, and diffusion models using the CPMA configuration settings as input. The trapezoidal and diffusion models are alternative transfer functions for CPMA that were derived theoretically by Olfert and Collins (2005) and Sipkens et al. (2020), respectively, based on slightly different assumptions from the triangular transfer function. For instance, the trapezoidal model assumes the axial flow to be parabolic and forces to vary radially, while the diffusion model incorporates particle diffusion into the models. The diffusion and trapezoidal models utilized here correspond to Sipkens et al.'s (2020) study.

For further insights into the trapezoidal and diffusion models, encompassing their theoretical derivations and numerical implementations, you are encouraged to read the work of Sipkens et al.'s (2020)