Laboratory experiments were conducted to generate empirical dimensionless correlations for estimating surface roughness of frost formed on a cold flat plate under forced convection. Environmental variables, including wall temperature $T_s$, air velocity $V_{\mathrm{air}}$, relative humidity $\mathrm{RH}$, and air temperature $T_{\mathrm{air}}$, were considered when generating the correlations. The test conditions were chosen to simulate the environmental conditions experienced by cold-soaked fuel frost formation on the upper surface of airplane wings. Experimental conditions included wall temperatures from $-20$ to $-5°\mathrm{C}$, freestream temperatures from 8 to $16°\mathrm{C}$, relative humidities from 60 to 91%, and air velocities from 0.5 to $2.5\mathrm{m}\cdot {\mathrm{s}}^{-1}$. The root-mean-square height, skewness, and equivalent sand-grain roughness height of frost were correlated as functions of the Reynolds number, absolute humidity, and dimensionless temperatures. The comparison between the correlation of frost equivalent sand-grain roughness height in this study and a previous model revealed the importance of test surface geometry on frost roughness formation.

进行了实验室实验以生成经验无量纲相关性，以估计强制对流下冷平板上形成的霜的表面粗糙度。环境变量，包括壁温${吨}_{秒}$, 风速 ${伏}_{\mathrm{空气}}$， 相对湿度 $\mathrm{相对湿度}$, 和空气温度 ${吨}_{\mathrm{空气}}$，在生成相关性时考虑。选择测试条件是为了模拟飞机机翼上表面冷浸燃料结霜所经历的环境条件。实验条件包括壁温从$-20$ 至 $——5°\mathrm{C}$, 自由流温度从 8 到 $16°\mathrm{C}$，相对湿度从 60% 到 91%，空气速度从 0.5 到 $2.5\mathrm{米}\cdot {\mathrm{秒}}^{-1}$. 霜的均方根高度、偏度和等效沙粒粗糙度高度与雷诺数、绝对湿度和无量纲温度的函数相关。本研究中霜等效沙粒粗糙度高度的相关性与先前模型的比较揭示了测试表面几何形状对霜粗糙度形成的重要性。