Heated transitional supersonic jets exhausting from a rectangular nozzle at over-expanded conditions are investigated by Large Eddy Simulations and Ffowcs-Williams and Hawkings acoustic analogy. Four cases with a fixed nozzle pressure ratio but different temperature ratios (TR) of 1.0, 2.0, 4.0, and 7.0 are analyzed. Numerical results show that with the increasing temperature the jet velocity significantly increases, whereas its Reynolds number decreases by about one order of magnitude, which leads to a 30% decrease in the jet potential core length and reduction in the number of shock cells. The increasing temperatures also result in supersonic shear layer convection Mach numbers and consequently Mach wave radiations in the acoustic fields. Pressure skewness and kurtosis factors indicate crackle noise and non-linear propagation effects in high temperatures. For the most heated jet TR 7.0, the Mach wave radiation is identified radiating noise at about 120 degrees, while the large turbulence structure noise at about 150 degrees. Furthermore, the vortex sheet model analysis and the LES data detect the existence of upstream-propagating neutral waves inside jet TR 7.0. The observed screech frequency falls within the range of antisymmetric mode indicating that the highly-heated jet is characterized by an antisymmetric oscillation mode at the screech frequency.

大型涡流模拟和Ffowcs-Williams和Hawkings声学模拟研究了在过度膨胀条件下从矩形喷嘴排出的加热的过渡超音速射流。分析了四种喷嘴压力比固定但温度比（TR）为1.0、2.0、4.0和7.0的情况。数值结果表明，随着温度的升高，射流速度显着增加，而其雷诺数却减少了大约一个数量级，这导致射流电势芯长度减少了30％，激波单元的数量减少了。温度升高还导致超声速剪切层对流马赫数，并因此导致声场中的马赫波辐射。压力偏斜度和峰度因子表明在高温下裂纹声和非线性传播效应。对于最热的射流TR 7.0，识别出马赫波辐射的辐射噪声约为120度，而大的湍流结构噪声约为150度。此外，涡旋片模型分析和LES数据检测到射流TR 7.0内部是否存在上游传播的中性波。所观察到的刺耳声频率落在反对称模式的范围内，这表明在刺耳声频率下，高热射流的特征在于反对称振荡模式。涡流板模型分析和LES数据检测到射流TR 7.0内部是否存在上游传播的中性波。所观察到的刺耳声频率落在反对称模式的范围内，这表明在刺耳声频率下，高热射流的特征在于反对称振荡模式。涡流板模型分析和LES数据检测到射流TR 7.0内部是否存在上游传播的中性波。所观察到的刺耳声频率落在反对称模式的范围内，这表明在刺耳声频率下，高热射流的特征在于反对称振荡模式。