CFD source terms

Surface Dielectric Barrier Discharge Designer · plot the body-force / energy source terms and export them as a ready-to-compile Fluent UDF.

SDBDesigner 由莫斯科物理技术学院 Victor Soloviev、Vladimir Krivtsov 教授和西安交通大学朱益飞教授联合研制，作为等离子体激励装置研发链条中的一环，基于充分验证的实验、物理和解析模型，准确计算放电特性和流体响应参数，支撑 SDBD 等离子体装置的结构、材料和电源选型。该工具涉及的推力和放电参数理论由 Victor Soloviev 教授和 Vladimir Krivtsov 教授首次提出，并由朱益飞教授和等离子体计算工坊团队发展、修正与闭环。

SDBDesigner is an online tool to calculate and design discharge and CFD parameters of surface dielectric barrier discharges. The theories are derived from Prof. Victor Soloviev and Prof. Vladimir Krivtsov [1,2] and further extended by Prof. Yifei ZHU [3] of PFC3M and Gongfang Group.

[1] V. R. Soloviev, "Analytical estimation of the thrust generated by a surface dielectric barrier discharge," J. Phys. D: Appl. Phys., vol. 45, no. 2, 2012.

[2] V. Soloviev and V. Krivtsov, "Analytical and numerical estimation of the body force and heat sources generated by the surface dielectric barrier discharge powered by alternating voltage," EUCASS2015, 2015.

[3] Y. Zhu and Y. Wu, "The secondary ionization wave and characteristic map of surface discharge plasma in a wide time scale," New J. Phys. 22, 103060 (2020).

Dielectric parameters

Dielectric thickness [m]

Substrate thickness [m]

Permittivity

SEE coefficient

Voltage parameters

Maximum voltage (V)

Rising time (s)

Frequency (Hz)

Voltage type

Sine Pulse

Gas parameters

Pressure (Pa)

Temperature (K)

Plasma parameters

Ion drift velocity (m/s)

Characteristic electric field (V/m)

Plasma layer thickness (m)

Cathode potential (V)

Ionization frequency (Hz)

Townsend coeff. A (V/cm/Torr)

Electron mobility (m2/V/s)

Townsend coeff. B (V/cm/Torr)

Source term equation

F = α·Thrust·x·y·exp(−x/X1 − y/Y1) / (X1²·Y1²)

Thrust (N/m)

X1 (m)

Y1 (m)

Q = Etotal·(1 − x/ls)·(y/hd)·exp(−y/hd)·(4/ls/hd)

Etotal (J/m³)

ls (m)

hd (m)

α is a streamwise switch (Heaviside step), not a physical coefficient: α = 0 for x < X1, α = 0.5 at x = X1, α = 1 for x > X1. It suppresses the body force upstream of X1 and applies it at full strength downstream.

Parameters can be programmed into CFD codes (PHengLEI, ANSYS CFX/Fluent UDF, …). The Fluent UDF export below wraps both source terms in ready-to-compile C. Set the actuator origin and orientation in your own mesh accordingly.

Source term plot

Body force density (N/m³)

Energy density (J/m³)

Click Plot source terms to render the source-term maps.

Parameter guide

Source terms

Body force F — momentum source density (N/m³) injected into the fluid; drives the induced wall jet.

Energy Q — energy source density (J/m³) deposited by the discharge.

X1 / Y1 — streamwise / wall-normal decay lengths of the body-force profile.

ls / hd — discharge length and plasma layer thickness scaling the energy source.

Export — X Y Z point cloud, ready-to-compile Fluent UDF, or the raw parameters for PHengLEI / CFX.

Dielectric

Dielectric thickness — distance between the buried electrode and the dielectric surface.

Substrate thickness — thickness of the material (e.g. glue) between exposed electrode and dielectric.

Permittivity — relative permittivity of the dielectric.

SEE coefficient — secondary electron emission coefficient of the dielectric.

Voltage

Maximum voltage — peak value of the applied voltage.

Rising time — time for the voltage to rise 0→peak. For a sine it equals 1/4 of the cycle, so it is derived from the frequency and not entered directly; for a pulse you set it yourself.

Frequency — for a sine, the input you set (rising time follows as 1/(4f)); for a pulse, the repetition rate, independent of rising time.

Voltage type — sinusoidal AC (Sine) or pulsed (Pulse).

Plasma

Ion drift velocity — V_dr = μ_i·E.

Characteristic field — E_c, proportional to gas density.

Cathode potential — cathode potential drop; ≈ 600 V for SDBD in air.

Townsend coeff. A / B — α_T = A·p·exp(−B·p/E).