Derivation of Turbulent Energy in Presence of Dust Particles

Abstract

Abstract:Energy equation for dusty fluid turbulent flow has been derived in terms of correlation tensors of second order.In presence of dust particles, mathematical modeling of turbulent energy is discussed including the correlation between the pressure fluctuations and velocity fluctuations at two points of the flow field, where the correlation tensors are the functions of space coordinates, distance between two points and time. To reveal the relation of turbulent energy between the two points, one point has been taken as origin of the coordinate system.

Conversion of Energy Equation for Turbulent Motion and its Applications

“…3. The gradient Richardson number is as a function of the ratio of the increase in potential energy to the decrease in kinetic energy which has been derived in equation (18) and the Fig. 4 states that the factor γ becomes smaller as the gradient Richardson number increasing everywhere.…”

“…So, the buoyancy flux and therefore the derived eddy coefficient are associated with the small scale turbulence. The flux Richardson number has been considered the values less than 0.15 used in the derivation of equation (17). Dissipation that occurs in well-mixed portions of the water column is not allied with its proportionate share of mass transport.…”

“…Two equations were also developed in presence of dust particles [14] and in a rotating system [15]. Derivation of turbulent energy was discussed with two-point correlation [16], and in presence of dust particles [17], in a rotating system [18] and in a rotating system with dust particles [19]. All the correlation tensors used in the developed equations were defined as the functions of space coordinates, distance between two points and time.…”

Theoretical Model Development for Energy Motion of Dusty Turbulent Flow of Fibre Suspensions in a Rotational Frame

“…A precise and exact calculation of the collision rate includes an accurate understanding of the collision rate impacts caused by turbulence and preferential or clustering particle concentrations. Several studies [13][14][15][16][17][18][19][20][21] have been carried out on the motion of the dusty turbulent flow. e characteristics of the dust particles [22][23][24][25] mainly rely on the particle size of the turbulence scale.…”

“…e motions between a particle of the fluid and the suspended fibre rely on fluid dynamics fundamental of turbulence characteristics with the velocity pressure correlations of fluctuating components. A good number of [15,[29][30][31][32][33][34][35] studies have been undertaken in rotating systems to analyze the motion of turbulent flows. e mean rotation induces dynamical influences on turbulent flows through the pressure-stream-rate correlation in the transport equations.…”