Model for Predicting Solids Velocity Fluctuations in Sedimenting Suspensions Computational fluid dynamics (CFD) simulations of sedimenting suspensions in two-dimensional periodic domains using a Eulerian two-fluid model were per- formed with the commercial software ANSYS Fluent â . Three particle systems belonging to Geldart groups A and B were selected to gather data on the solids velocity fluctuations. It is proposed that solids velocity fluctuations are composed of local and global parts. Therefore, the solids velocity signal was segregated into low-frequency and high-frequency fluctuations using the FFT solver in MATLAB â . A model is proposed to predict the velocity fluctuations of a solid phase at low volume fractions and the model results are compared with the CFD results. The model is capable of capturing the solid particles fluctuation in the dilute limit. Keywords: Computational fluid dynamics, Fluctuations, Fluidization, Sedimentation, Two-fluid model Received: February 27, 2019; revised: July 22, 2019; accepted: September 06, 2019 DOI: 10.1002/ceat.201900147 1 Introduction Fluidized beds have found widespread use in the process indus- try, e.g., in the chemical, biochemical, energy, environmental, and food sectors [1]. In a typical fluidized bed, sufficient fluid is allowed to flow upwards through the bed of particles to cre- ate enough drag force to balance the weight force of the partic- ulate solids present. If the flow of the fluid is further increased, the bed of particles may expand in a way that the mean solids volume fraction remains uniform throughout the bed [2]. In real practice, however, this is seldom realized. Instead, with the increase of the fluid flow rate, the bed becomes unstable and inhomogeneities appear as concentration waves set in [2–7]. This instability is more pronounced if the operating fluid is a gas. In case of a heavily loaded gas fluidized bed, bubble-like structures have been observed and reported [6, 8–12]. How- ever, if one keeps on increasing the gas velocity for a fixed quantity of solids or decreasing the number of solid particles to be suspended for a fixed gas velocity, the gas bubbles may increase in size and number to a point at which point they form a continuous phase. Under such operating conditions, the particles arrange themselves to form dispersed clusters or streamers. Such solid-rich clusters have been observed experi- mentally in what is known as fast fluidization and pneumatic transport regimes [11–15]. The characteristic form or structure is mainly dependent on the volume fraction of the suspended solid particles. Several works have been done to explore and characterize the nature of the solids velocity fluctuations in liquids [16–22]. Essentially, the appearance of inhomogeneities in the fluidized beds imparts horizontal and vertical velocities to the bed. As a result, the bed develops regions of nonuniformity [23]. A lot of work has been done on the qualitative and quantitative assess- ment of the velocity fluctuations in sedimentations and suspen- sions, both computationally and experimentally, and various models have been proposed. This includes the works of Segre ` et al. [19], Nicolai and Herzhaft [20], Ladd [24], Padding and Louis [25], Climent and Maxey [26], Hamid et al. [27], and many more. However, investigations of the velocity fluctua- tions in a fluidized bed have received lesser attention. Cowan et al. [22] studied the velocity fluctuations in fluidized suspen- sions using ultrasonic correlation spectroscopy. Gevrin et al. [28] evaluated the two-fluid formulation for numerical model- ing of liquid fluidized beds by studying granular pressure and particle velocity fluctuations. Zivkovic et al. [29] investigated the granular temperature rise due to particle velocity fluctua- tions in a liquid fluidized bed, using diffusing wave spectros- copy. However, it is established that a fluidized bed of solid particles is simply a cloud of sedimenting particles referred to Chem. Eng. Technol. 2019, 42, No. 00, 1–9 ª 2019 WILEY-VCH Verlag GmbH & Co. KGaA www.cet-journal.com Ali Shehryar 1 Aitazaz Hassan 2 Adnan Hamid 2 Celso Murilo dos Santos 3 Afrasyab Khan 4 Atta Ullah 2, * – 1 Ali Shehryar Pakistan Institute of Engineering and Applied Sciences (PIEAS), Department of Mechanical Engineering, Nilore, Islamabad, Pakistan. 2 Aitazaz Hassan, Dr. Adnan Hamid, Dr. Atta Ullah atta@pieas.edu.pk Pakistan Institute of Engineering and Applied Sciences (PIEAS), Department of Chemical Engineering, Nilore, Islamabad, Pakistan. 3 Celso Murilo dos Santos University of Blumenau, Department of Chemical Engineering, Blumenau, Brazil. 4 Dr. Afrasyab Khan Department of Management of Science and Technology Develop- ment, Faculty of Civil Engineering, Ton Duc Thang University (TDTU), Ho Chi Minh City, Vietnam. Research Article 1 These are not the final page numbers! ((