Pressure-velocity coupling

For the computation of compressible flow, the pressure-velocity coupling schemes previously described can be extended to pressure-velocity-density coupling schemes. Again, a solution of the linearized, compressible momentum equation obtained with the pressure and density values taken from a previous solver iteration in general does not satisfy the mass balance equation. In order to balance the mass fluxes into each volume element, a pressure, density and velocity correction on top of the old values is computed. Typically, the detailed algorithms for performing this task rely on the same approximations such as the SIMPLE or SIMPLEC schemes outlined in the previous paragraph. 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

P 61] The numerical simulations were based on the solution of the incompressible Navier-Stokes equation and a convection-diffusion equation for a concentration field by means of the finite-volume method [152], The Einstein convention of summation over repeated indices was used. For pressure-velocity coupling, the SIMPLEC algorithm and for discretization of the species concentration equation the QUICK differencing scheme were applied. Hybrid and the central differencing schemes referred to velocities and pressure, respectively (commercial flow solvers CFX4 and CFX5). 

Jang, D.S., Jetli, R. and Acharya, S. (1986), Comparison of the PISO, SIMPLER and SIMPLEC algorithms for the treatment of the pressure velocity coupling in steady flow problems. Numerical Heat Transfer, 19, 209-228. 

In this approach, the finite volume methods discussed in the previous chapter can be applied to simulate the continuous fluid (in a Eulerian framework). Various algorithms for treating pressure-velocity coupling, and the discussion on other numerical issues like discretization schemes are applicable. The usual interpolation practices (discussed in the previous chapter) can be used. When solving equations of motion for a continuous fluid in the presence of the dispersed phase, the major differences will be (1) consideration of phase volume fraction in calculation of convective and diffusive terms, and (2) calculation of additional source terms due to the presence of dispersed phase particles. For the calculation of phase volume fraction and additional source terms due to dispersed phase particles, it is necessary to calculate trajectories of the dispersed phase particles, in addition to solving the equations of motion of the continuous phase. 

The fractional-step concept can be used to solve the governing equations for the fluid motion as well. To illustrate the overall method with emphasis on the pressure-velocity coupling, a FVM variant of the fractional-step method used by Chorin [30], Fortin et al [56] and Andersson and Kristoffersen [3] for solving the unsteady Navier-Stokes and continuity equations for incompressible viscous flows is outlined. We consider the equations of motion of an incompressible viscous fluid ... 

Based on the finite volume method, the control equation can be converted to a numerical method for solving algebraic equations. Convection of equation use second-order upwind difference during the discrete process, the solver is based on the pressure, the pressure-velocity coupling adopt the SIMPLE algorithm, pressure interpolation scheme use PRESTO Format. 

Since the velocities obtained in the previous step may not satisfy the continuity equation, one more equation for the pressure correction is derived from the continuity equation and the linearised momentum equations once solved, it gives the correct pressure so that continuity is satisfied. The pressure-velocity coupling is made by the simple algorithm, as in FLUENT default options. 

In most cases, the flow is considered isobaric, such that Eq. (3.6) reduces to p=p x = 0, t). This is a key simplification that removes the strong pressure-velocity coupling and the time integration limitations associated with the compressible flow equations. The isobaric assumption is in most cases... 

The model equations were solved numerically by using the commercial software FLUENT 6.2 with finite volume method. The SIMPLEC algorithm was used to solve the pressure-velocity coupling problem in the momentum equations. The second-order upwind spatial discretization scheme was employed for all differential equations. 

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