This study aims to overcome the problems that existing background-oriented schlieren (BOS) techniques based on computed tomography (CT-BOS) face when measuring pressure fields of laser-induced underwater shock waves. To do this, it proposes a novel BOS technique based on vector tomography (VT-BOS) of an axisymmetric target. The remarkable feature of the proposed technique is the reconstruction of an axisymmetric vector field with nonzero divergence, such as the field of a laser-induced underwater shock wave. This approach is based on an approximate relation between the projection of the axisymmetric vector field and the reconstructed vector field. For comparison, the pressure fields of underwater shock waves are measured with VT-BOS, CT-BOS, and a needle hydrophone. It is found that VT-BOS is significantly better than CT-BOS in terms of better convergence, less dependence on the spatial resolution of the acquired images, and lower computational cost. The proposed technique can be applied not only to fluid dynamical fields, but also to other axisymmetric targets in other areas, such as electromagnetics and thermodynamics.
Graphical abstract
This study aims to overcome the problems that existing background-oriented schlieren (BOS) techniques based on computed tomography (CT-BOS) face when measuring pressure fields of laser-induced underwater shock waves. To do this, it proposes a novel BOS technique based on vector tomography (VT-BOS) of an axisymmetric target. The remarkable feature of the proposed technique is the reconstruction of an axisymmetric vector field with nonzero divergence, such as the field of a laser-induced underwater shock wave. This approach is based on an approximate relation between the projection of the axisymmetric vector field and the reconstructed vector field. For comparison, the pressure fields of underwater shock waves are measured with VT-BOS, CT-BOS, and a needle hydrophone. It is found that VT-BOS is significantly better than CT-BOS in terms of better convergence, less dependence on the spatial resolution of the acquired images, and lower computational cost. The proposed technique can be applied not only to fluid dynamical fields, but also to other axisymmetric targets in other areas, such as electromagnetics and thermodynamics.
A high-resolution background-oriented schlieren (BOS) technique, which utilizes a high-resolution camera and a microdot background pattern, is proposed and used to measure the pressure field of an underwater shock wave in a microtube. The propagation of the shock wave subsequently reaches a concave water–air interface set in the microtube resulting in the ejection of a focused microjet. This high spatial-resolution BOS technique can measure the pressure field of a shock front with a width as narrow as the order of only $$10^1\,\upmu$$
10
1
μ
m with a peak pressure as large as almost 3 MPa. This significant breakthrough has enabled the simultaneous measurement of the pressure impulse of the shock front and the velocity of the microjet tip. As a result, we have experimentally observed the linear relation between the velocity of the microjet tip and the pressure impulse of the shock front for the cases without secondary cavitation in the liquid bulk. Such relation was theoretically/numerically predicted by Peters et al. (J Fluid Mech 719:587–605, 2013). This study demonstrated the capability of the proposed high-resolution BOS technique as a microscale contactless pressure measurement tool for underwater shock waves and potentially other micro- and nanofluids.
Graphical abstract
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