<p>Analytical models are among the most direct and efficient methods for predicting jet behavior in engineering and practical applications. Based on Reichardt’s hypothesis, the momentum transformation equation for a single free jet was derived. Using a superposition approach, the momentum distribution for multiple jets was determined, enabling the development of a three-dimensional analytical model for multiple parallel jets. The effectiveness of this superposition technique in predicting the mean streamwise velocity components of multiple jets was validated through a combination of experimental and numerical simulations. For non-parallel jets, interactions between jets result in deflections as they enter the flow field, introducing the concept of a“velocity deflection interface”. Due to experimental limitations, accurately determining the position of the velocity deflection interface is challenging, making numerical simulations the preferred approach. The Shear-Stress transport (SST) k-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\upomega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">ω</mi> </math></EquationSource> </InlineEquation> turbulence model was employed, and jet angles between 1<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> and 20<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(^\circ \)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∘</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> , commonly used in industrial applications, were analyzed. By fitting data along the flow direction, the position of the velocity deflection interface was identified, and its relationship with the jet angle was established. In the upstream region of the velocity deflection interface, the relationship between the velocity deflection interface and the initial jet exit characteristics was quantified. In the downstream region, the parallel jet theory based on Reichardt’s hypothesis was extended to derive analytical equations for three-dimensional non-parallel jets. Finally, a comparison of jet analysis results with experimental data and computational fluid dynamics (CFD) simulations confirmed the validity of the analytical model. It provides theoretical support for predicting the behavior of multiple jets in engineering applications.</p>

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A three-dimensional analytical model for multiple jets based on reichardt’s hypothesis and velocity deflection interface concept

  • Fengsheng Qi,
  • Liangyu Zhang,
  • Deqiang Li,
  • Xudong Tang,
  • Zhongqiu Liu,
  • Sheraman C. P. Cheung,
  • Baokuan Li

摘要

Analytical models are among the most direct and efficient methods for predicting jet behavior in engineering and practical applications. Based on Reichardt’s hypothesis, the momentum transformation equation for a single free jet was derived. Using a superposition approach, the momentum distribution for multiple jets was determined, enabling the development of a three-dimensional analytical model for multiple parallel jets. The effectiveness of this superposition technique in predicting the mean streamwise velocity components of multiple jets was validated through a combination of experimental and numerical simulations. For non-parallel jets, interactions between jets result in deflections as they enter the flow field, introducing the concept of a“velocity deflection interface”. Due to experimental limitations, accurately determining the position of the velocity deflection interface is challenging, making numerical simulations the preferred approach. The Shear-Stress transport (SST) k- \(\upomega \) ω turbulence model was employed, and jet angles between 1 \(^\circ \) and 20 \(^\circ \) , commonly used in industrial applications, were analyzed. By fitting data along the flow direction, the position of the velocity deflection interface was identified, and its relationship with the jet angle was established. In the upstream region of the velocity deflection interface, the relationship between the velocity deflection interface and the initial jet exit characteristics was quantified. In the downstream region, the parallel jet theory based on Reichardt’s hypothesis was extended to derive analytical equations for three-dimensional non-parallel jets. Finally, a comparison of jet analysis results with experimental data and computational fluid dynamics (CFD) simulations confirmed the validity of the analytical model. It provides theoretical support for predicting the behavior of multiple jets in engineering applications.