## 1 Introduction  
Rapid development in the fields of computer technology, manufacturing techniques and materials science makes the geometry of key components more complex. For example, instead of an assembly of a disk and removable blades, the integratedbladed disk (BLISK) technology has been widely applied in the aeroengine design due to the merits of a light weight, high aerodynamic efficiency, excellent fatigue resistance and high efficiency of fuel consumption [1]. Recently, such monocoue components have been conveniently designed and fabricated by the emerging additive manufacturing (AM), also known as 3D printing technology. Although AM has an excellent ability to manufacture complex-shaped parts with an optimal structure design, the quality of manufactured products may be influenced by buckling, residual stress and internal defects during the cooling process [2]. Moreover, there is a higher tendency to bring in defects in complex-shaped parts due to a much greater surface area. Therefore, to guarantee the safety of these key components, special attention should be paid to the quantitative nondestructive testing (NDT) of complex-shaped parts. X-ray computed tomography (XCT) is widely used to inspect such parts in an industrial application. Although XCT possesses a high sensitivity to volumetric defects such as gas pores and inclusions, it is insensitive to planar defects such as cracks and delamination [3]. In addition, a high energy X-ray source is required for thick metals, resulting in radiation hazards and expensive equipment. On the other hand, ultrasound plays an irreplaceable role in NDT with the advantages of a large penetration depth, large area coverage and high sensitivity to both internal and surface defects. Both a single transducer with a scanning system and a transducer array have been widely applied to develop methods to visualize ultrasonic results with various imaging algorithms. Synthetic imaging methods including a common source method (CSM) [4; 5], a synthetic aperture focusing technique (SAFT) and a total focusing method (TFM) [6; 7] have been well developed to produce high resolution images for the objects below the measurement based on the wave reflections. However, when the surface of the tested object is uneven or irregular, the deployment of contact transducers will be difficult and poor coupling will lead to inaccurate or false detection. Currently, there are three common schemes to tackle this issue. The first method is to integrate the transducer with a wedge or \"shoe\" to match the surface to allow direct contact. This method is indeed simple but a wedge is only suitable for one specific surface. When the surface profile is varying or too complex, this method is difficult or even impossible to apply. The second method is to use flexible transducers [8], which show a greater compatibility than wedges. However, a few potential defects may go undetected in the dead zone because of the near field. The third method is to place the tested object into a water-filled chamber and the water acts as an acoustic couplant [9]. As a whole water-filled regular structure, objects with highly curved surfaces can be inspected. However, there is a large difference of acoustic impedance between the water and metal materials that hinders ultrasonic energy from effectively penetrating into the tested metal object. Thus, the performance is limited for metal parts with complex shapes. Recently, to bridge the gap between the immersion method and the contact method, [PERSON] et al. proposed a cryo-ultrasonic method to inspect complex-shaped parts, which were encased in ice with a cylinder container [10]. As the longitudinal wave speed of ice is about 2.5 times that of water, the acoustic impedance mismatch with the metal material can be greatly reduced so that the transmission energy will significantly increase. Their preliminary results demonstrated its superiority compared with the immersion method.