Conservation laws and conserved quantities of the governing equations for the laminar wake flow behind a small hump on a solid wall boundary

Julyan, Jonathan; Hutchinson, A.J.

doi:10.1016/j.ijnonlinmec.2018.01.011

Cited by 4 publications

(8 citation statements)

References 20 publications

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“…CTBS is a Bingham plastic fluid 39,40 . The energy conservation equation (Bernoulli's principle), the momentum equation, the continuity equation and the equation of state of particle motion could be derived by introducing different constitutive relation calculations which are consistent with the CTBS 41–44 . (as shown in Equations 1–4)

{z}_1+\frac{p_1}{\gamma }+\frac{v_1^2}{2g}={z}_2+\frac{p_2}{\gamma }+\frac{v_2^2}{2g}+h

\rho \frac{dv}{dt}=-\nabla p+\rho F+{\eta}_0\varDelta v

\frac{\partial \rho }{\partial t}+\nabla \cdot \overset{\rightharpoonup }{v}=0

m\frac{dv}{dt}= vg\left({\rho}_p-\rho \right)- CA\rho \frac{v^2}{2}

Where z 1 , z 2 is the height of different positions of CTBS.…”

Section: Methodsmentioning

confidence: 99%

Flow visualization simulation of cemented tailings backfill slurry by particle tracking technology

Sun

Gan

Zhi

et al. 2022

Engineering Reports

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Pipeline flow visualization of cemented tailings backfill slurry (CTBS) improves the safety and stability of transportation. High turbidity and low resolution make it difficult for conventional methods to monitor the particle distribution state of CTBS in a short period of time. Particle tracking technology (PTT) is used to simulate and investigate the flow characteristics of CTBS pipeline, combine with theoretical analysis to construct a CTBS pipeline visualization model, elaborate the particle distribution state when CTBS flows in the pipeline, and explore the effects of pipe diameter (PD), flow velocity (FV) and tailings gradation (TG) on the particle distribution. The results show that particle tracking technology is better applied to investigate the particle transport distribution characteristics of CTBS tailings. Three concepts of particle accumulated gravity Ga, static friction angle θ and diameter dividing line are defined, and the transport pipe is divided into light wear zone, medium wear zone and heavy wear zone. The increase in pipe diameter increases the content of fine particles at the pipe wall and the thickness of the lubrication layer becomes larger, which improves the safety and stability of CTBS transport. The increased flow velocity reduces the settling phenomenon of large size particles and improves the transport efficiency, which increases the pipeline transport resistance. Under good tailings grading conditions, a wide range of tailings grading is more suitable as backfill material. The results of the study illustrate the flow characteristics of the backfill slurry in the pipeline from the particle perspective and provide a theoretical basis for pipeline transportation research.

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{z}_1+\frac{p_1}{\gamma }+\frac{v_1^2}{2g}={z}_2+\frac{p_2}{\gamma }+\frac{v_2^2}{2g}+h

\rho \frac{dv}{dt}=-\nabla p+\rho F+{\eta}_0\varDelta v

\frac{\partial \rho }{\partial t}+\nabla \cdot \overset{\rightharpoonup }{v}=0

m\frac{dv}{dt}= vg\left({\rho}_p-\rho \right)- CA\rho \frac{v^2}{2}

Where z 1 , z 2 is the height of different positions of CTBS.…”

Section: Methodsmentioning

confidence: 99%

Flow visualization simulation of cemented tailings backfill slurry by particle tracking technology

Sun

Gan

Zhi

et al. 2022

Engineering Reports

View full text Add to dashboard Cite

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“…When the slurry flow state is laminar flow, the flow process follows to laminar energy equation, momentum equation, continuity equation and particle motion state equation [21,22].…”

Section: Governing Equationmentioning

confidence: 99%

Numerical Investigation of Evolution Characteristics of Ultrafine Tailings Backfill Slurry Flow Considering Slurry Temperature

2023

Teh. vjesn.

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To analyze the effect of slurry temperature on Ultrafine tailings backfill slurry (UTBS) flow characteristics, a new comprehensive Reynolds number (Rc) model considering slurry temperature for determining the flow pattern of UTBS was proposed. The flow evolution characteristics of UTBS considering the effect of slurry temperature were investigated under the condition of coupled multi-physical fields. UTBS flow velocity field was divided into shear zone and structural flow zone. With the flow proceeded, the area of the structural flow zone decreased. Increasing slurry temperature could generate more gel, which could wrap the tailings particles and reduce the resistance loss. When transport flow increased, the interaction between UTBS particles and friction increased, which caused the resistance loss to increase. Influenced by "non-uniform interference settlement" and the law of tailing sand particle transport, the resistance loss increased with the increase of stowing gradient. This paper suggests that the mine could choose a transport flow rate of 220 m 3 /h and stowing gradient of 5 as a reference for pipeline transport.

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“…e equations that modeled the flow problem along with their conditions are given here. Continuity (8) will reduce to identity with velocity given in (1). After some mathematical simplifications, modeled equations reduce to…”

Section: Governing Equationsmentioning

confidence: 99%

“…In this communication, we have described the transport of momentum, heat, and concentration with the help of mathematical relations. Mathematical relations are formulated with constitutive expressions that handle fluxes of the above-prescribed quantities [1]. Formulated equations, remained helpful to analyze the transport of heat, diffusion of chemical species, movement of geological flows, engineering applications, meteorology, material science, and medicines [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…Formulated equations, remained helpful to analyze the transport of heat, diffusion of chemical species, movement of geological flows, engineering applications, meteorology, material science, and medicines [2,3]. Molecular contact and Brownian motion [1] characterized the conductivity, diffusivity, and viscosity for the nanofluid in the flow domain. Particularly, transfer of heat is an analog of mass transfer in the constitutive expressions for fluxes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

Anwar¹,

Irfan

Hussain

et al. 2022

Mathematical Problems in Engineering

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This study examines viscoelastic fractional nanofluid flow through Darcy medium. Memory characteristics due to elasticity are explored with noninteger time derivatives. The unsteady motion of MHD flow is modeled by nonlinear differential equations. Buoyancy forces are incorporated via convection parameters in the flow domain. Fractional relaxation time is considered to control the propagation speed of temperature. A finite difference, along with finite element, a numerical algorithm has been developed for the computation of governing flow equations. Friction coefficient, Sherwood numbers, and Nusselt numbers are computed for the noninteger derivative model. Simulations revealed that noninteger numbers have congruous behavior for concentration, temperature, and velocity fields. It is also noted that heat flux, δ 1 , and mass flux, δ 2 , numbers have contradictory effects on the friction coefficient. Various flows, particularly in polymer industries and electrospinning for the production of nanofibers, can be tackled in a comparable pattern.

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Conservation laws and conserved quantities of the governing equations for the laminar wake flow behind a small hump on a solid wall boundary

Cited by 4 publications

References 20 publications

Flow visualization simulation of cemented tailings backfill slurry by particle tracking technology

Flow visualization simulation of cemented tailings backfill slurry by particle tracking technology

Numerical Investigation of Evolution Characteristics of Ultrafine Tailings Backfill Slurry Flow Considering Slurry Temperature

Heat Transfer in a Fractional Nanofluid Flow through a Permeable Medium

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