This paper presents a multiphase turbulence closure employing one transport equation, namely, the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A double-time averaging approach for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less restrictive assumptions comparative to the previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

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