Scaling Law for Thermo‑Mechanical Responses of Metal Plate Subjected to Laser Irradiation Under High‑Speed Airflow Condition

Yue Cui; Ruixing Wang; Te Ma; Wu Yuan; Hongwei Song; Chenguang Huang

doi:10.3788/CJL231077

Chinese Journal of Lasers, Volume. 51, Issue 12, 1202103(2024)

Scaling Law for Thermo‑Mechanical Responses of Metal Plate Subjected to Laser Irradiation Under High‑Speed Airflow Condition

Yue Cui^1,3, Ruixing Wang^1,3、*, Te Ma^1,3, Wu Yuan^1,2,3, Hongwei Song^1,2,3, and Chenguang Huang³

Author Affiliations

¹Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

²Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

³School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(11)

Fig. 1. Experimental validation of the multifield coupling analysis method. (a) Comparison for time evolution of temperature between simulated and experimental results; (b) error

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Fig. 2. Temperature history curves of the laser spot center under different scaling factors. (a) 1/2 scaling; (b) 1/4 scaling

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Fig. 3. Equivalent strain passing through the direction of the airflow under different scaling factors. (a) 1/2 scaling; (b) 1/4 scaling

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Fig. 4. Comparison of temperature and strain field diagrams of metal plate under different scaling factors (half model). (a) Temperature field; (b) strain field

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Fig. 5. Temperature history curves of the laser spot center under different Mach numbers

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Fig. 6. Equivalent strain passing through the direction of the airflow under different Mach numbers

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Fig. 7. Comparison of temperature and strain field diagrams of metal plate under different Mach numbers (half model). (a) Temperature field; (b) strain field

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Table 1. Similarity criteria and guidelines

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Table 1. Similarity criteria and guidelines

No.	Similarity criteria	Simplified conditions	Similarity criteria	Physical explanation
1	$\frac{k_{0} t_{0}}{ρ_{0} C_{p} l_{0}^{2}}$	The model materials are unchanged	$\frac{t_{0}}{l_{0}^{2}}$	The ratio of the laser irradiation time to the square of the geometric dimension is unchanged
2	$f_{0} l_{0}$		$f_{0} l_{0}$	The body force is multiplied by the geometric dimension
3	$\frac{E_{0} u_{0}}{l_{0}}$	The model materials are unchanged	$\frac{u_{0}}{l_{0}}$	The deformation field is divided by the geometric dimension
4	$E_{0} θ_{0}$	The model materials are unchanged	$θ_{0}$	Strain fields are unchanged
5	$E_{0} α_{0} T_{0}$	The model materials are unchanged	$T_{0}$	Temperature fields are unchanged
6	$\frac{χ_{0} Q_{0} l_{0}}{k_{0} T_{0}}$	The temperature fields and model materials are unchanged	$Q_{0} l_{0}$	The laser power density is multiplied by geometric size
7	$\frac{A {(\frac{ρ_{0}^{a i r} v_{0} l_{0}}{μ_{0}})}^{m} {(\frac{C_{p}^{a i r} μ_{0}}{λ_{a i r 0}})}^{n} λ_{a i r 0}}{k_{0}}$	The temperature fields，gas velocity and model materials are unchanged	$ρ_{0}^{a i r} l_{0}$	The density of gas is multiplied by geometric size
8	$\frac{P_{0}}{E_{0} θ_{0}}$	The strain fields and model materials are unchanged	$ρ_{0}^{a i r}$	The density of gas is unchanged

Table 2. Scaling law of structural response under combined action of laser and airflow (when the dimension is scaled by α)

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Table 2. Scaling law of structural response under combined action of laser and airflow (when the dimension is scaled by α)

Parameter		Scaling
Laser load	Laser beam diameter d₀	α
	Laser power density Q₀	1/α
	Irradiation time t₀	α²
Thermo-mechanical responses	Temperature T₀	1
	Deformation u₀	α
	Strain field θ₀	1
Parameters of high-speed airflow	Mach number Ma	1
	Static temperature T_s	1
	Static pressure P_s	1/α
	Density ρ	1/α
	Thermal conductivity λ $_{a i r}$	1
	Viscosity μ	1

Table 3. Thermophysical parameters of aluminum alloy

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Table 3. Thermophysical parameters of aluminum alloy

Temperature /K	Thermal conductivity / （W·m^-1·K^-1）	Specific heat /（J·kg^-1·K^-1）	Coefficient of thermal expansion /（10^-6·K^-1）	Young’s modulus / GPa	Poisson’s ratio	Density / （g·cm^-3）
293	155	900	21.4	68	0.31	2.85
373	159	921	23.1	64	0.31	2.85
473	163	1047	25.2	54	0.31	2.85
573	163	1130	26.8	42	0.31	2.85
673	159	1172	28.4	29	0.31	2.85

Table 4. Simulation conditions

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Table 4. Simulation conditions

Condition No.	Mach number	Static pressure /Pa	Density / （kg·m^-3）	Laser power density /（W·cm^-2）	Irradiation time /s	Scaling
1	Ma 0.8	74130	1.01	188	10	1（real model）
2	Ma 0.8	148260	2.02	376	2.5	1/2
3	Ma 0.8	74130	1.01	376	2.5	1/2
4	Ma 3.0	74130	1.01	188	10	1（real model）
5	Ma 3.0	148260	2.02	376	2.5	1/2
6	Ma 3.0	74130	1.01	376	2.5	1/2
7	Ma 3.0	296520	4.04	752	0.625	1/4
8	Ma 3.0	74130	1.01	752	0.625	1/4

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Yue Cui, Ruixing Wang, Te Ma, Wu Yuan, Hongwei Song, Chenguang Huang. Scaling Law for Thermo‑Mechanical Responses of Metal Plate Subjected to Laser Irradiation Under High‑Speed Airflow Condition[J]. Chinese Journal of Lasers, 2024, 51(12): 1202103

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Paper Information

Category: Laser Forming Manufacturing

Received: Aug. 1, 2023

Accepted: Sep. 5, 2023

Published Online: Feb. 26, 2024

The Author Email: Wang Ruixing (wangruixing@imech.ac.cn)

DOI:10.3788/CJL231077

CSTR:32183.14.CJL231077

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology