熱防護系統材料廣泛應用於航空太空和國防領域。它們利用輻射（例如陶瓷）、熱解（例如三元乙丙橡膠）和熱沉（例如鎢、石墨、銅）等機制去除熱能以提供熱保護。如果能夠建立熱防護材料的侵蝕/燒蝕/腐蝕模型，將能夠為極音速載具、火箭和垂直發射系統提供設計依據，還能為熱防護系統材料的選擇提供可靠的模擬結果。為此，本研究建立一個數學模型框架以模擬在超音速氣體-粒子兩相排氣羽流沖擊流場中熱防護材料的複雜物理化學機制。透過數學模型框架將能研究熱防護材料模型並在SRM環境中的侵蝕/燒蝕/腐蝕過程。該架構包含流場模型和材料的物理化學模型，並提供介面耦合方法，可將熱防護材料的物理化學模型與流場模型耦合。
為了研究熱防護材料長時程的熔化燒蝕問題，本研究採用了兩種分析策略來研究銅試樣板在縮尺管道式發射器中的熔融-燒蝕過程。通過比較雙向流體-熱-燒蝕耦合分析策略和雙向流體-熱-燒蝕鬆散耦合分析策略，確認了鬆散耦合分析策略的模擬結果的可靠性。此外，通過比較流體-熱-燒蝕鬆散耦合分析策略的模擬結果和林文山團隊實驗規模試驗的實驗結果，驗證了流體-熱-燒蝕鬆散耦合分析策略的模擬結果準確性。
研究結果顯示，在燃燒時間為3.6秒時，通過雙向流體-熱消融鬆散耦合分析策略所預測的銅試樣板的背板溫度分布與實驗結果接近。除此之外，採用鬆散耦合分析策略，可以在保持一定的計算結果精度的同時，降低計算成本。另外，模擬結果顯示燃燒時間為3.6秒時，通過雙向流體-熱消融鬆散耦合分析策略預測的消融深度曲線與實驗結果有很好的一致性，這為鬆散耦合分析策略的模擬結果提供了可靠性。
整體而言，熱防護材料在超音速氣體-顆粒雙相撞擊流中的熔化燒蝕問題可以通過鬆散耦合分析策略來預測熱防護材料的燒蝕深度剖面，並大大減少模擬所需的計算時間。最重要的是，在無法進行反熱傳導分析（IHCA）的情況下，通過鬆散耦合分析策略獲得的熱防護材料的衝擊表面熱通量可以作為估算進入熱防護材料表面的熱通量的手段。

Thermal protection system (TPS) materials are widely used in the aerospace and national defense fields. Mechanisms such as radiation (e.g. Ceramics), pyrolysis (e.g. Ethylene Propylene Diene Monomer, EPDM), and heat sink (e.g. Tungsten, Graphite, Copper) are used to remove thermal energy to provide thermal protection. If the erosion/ablation/corrosion model of the TPS material can be established, it will not only provide a design basis for hypersonic vehicles, rockets, and vertical launch systems but also offer reliable simulation results for the selection of TPS materials. To this end, a mathematical model framework is developed to simulate the complex physicochemical mechanisms of thermal protection material (TPM) in a supersonic gas-particle two-phase exhaust plume impingement flowfield. The mathematical model framework will enable the investigation of erosion/ablation/corrosion process of thermal protection materials in the solid rocket motor (SRM) environment. The framework contains the flow field model and the material physicochemical model and provides interface coupling methods by which the physicochemical model of the material can be coupled with the flow field model.
In order to investigate the long-duration of melt-ablation behavior of thermal protection material, two analysis strategies are used to investigate the melt-ablation process of the copper specimen plate in the scaled ducted launcher. The reliability of the simulation result for the two-way fluid-thermal-ablation loosely coupled analysis strategy is confirmed by comparing the two-way fluid-thermal-ablation coupled analysis strategy with two-way fluid-thermal-ablation loosely coupled analysis strategy. Furthermore, the accuracy of the fluid-thermal-ablation loosely coupled analysis strategy is validated by comparing the simulation results of the fluid-thermal-ablation loosely coupled analysis strategy and experimental results from Lin's team.
The simulation results show that the temperature distribution of the backside surface of copper impinging plate for two-way fluid-thermal-ablation loosely coupled analysis strategy is close to the experimental results of Lin’s team at burn time of 3.6 seconds. In addition, the use of the two-way fluid-thermal-ablation loosely coupled analysis strategy can reduce computational cost while maintaining a certain level of computational accuracy. The study result shows that the ablation depth profile predicted by two-way fluid-thermal-ablation loosely coupled analysis strategy at burn time of 3.6 seconds is in agreement with the experiment, which provides the reliability of the simulation results of the fluid-thermal-ablation loosely coupled analysis strategy.
In general, the melt-ablation problems of thermal protection materials in supersonic gas-particle two-phase impingement flow can be predicted by the fluid-thermal-ablation loosely coupled analysis strategy to predict the ablation depth profile of thermal protection material and greatly reduce the computation time required for the simulation. Most importantly, the impingement surface heat flux of the thermal protection material obtained by the two-way fluid-thermal-ablation loosely coupled analysis strategy can be used as a method to estimate the heat flux into the surface of the thermal protection material when inverse heat conduction analysis (IHCA) cannot be conducted.

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