source: branches/gui/sample/miscellaneous/tenprobs/prob05.mso @ 832

#*---------------------------------------------------------------------
* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
*
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* it under the therms of the ALSOC FREE LICENSE as available at
* http://www.enq.ufrgs.br/alsoc.
*
* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
* from http://www.rps.eng.br Copyright (C) 2002-2004.
* All rights reserved.
*
* EMSO is distributed under the therms of the ALSOC LICENSE as
* available at http://www.enq.ufrgs.br/alsoc.
*
*----------------------------------------------------------------------
* 5. Terminal velocity of falling particles
*----------------------------------------------------------------------
*
*   Description:
*      This problem is part of a collection of 10 representative
*       problems in Chemical Engineering for solution by numerical methods
*       developed for Cutlip (1998).
*
*   Subject:
*       * Fluid Dynamics
*
*       Concepts utilized:
*               Calculation of terminal velocity of solid particles falling in
*       fluids under the force of gravity.
*
*       Numerical method:
*               * Single nonlinear algebraic equation
*
*   Reference:
*       * CUTLIP et al. A collection of 10 numerical problems in 
*       chemical engineering solved by various mathematical software 
*       packages. Comp. Appl. in Eng. Education. v. 6, 169-180, 1998. 
*       * More informations and a detailed description of all problems
*       is available online in http://www.polymath-software.com/ASEE
* 
*----------------------------------------------------------------------
* Author: Rodolfo Rodrigues
* GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation, 
*                                       Control, and Optimization of Processes
* $Id$
*--------------------------------------------------------------------*#
using "types";



Model problem
        PARAMETERS
        g               as acceleration (Brief="Accelaration of gravity", Default=9.80665);
        
        
        VARIABLES
        vt              as velocity             (Brief="Terminal velocity");
        rho_p   as dens_mass    (Brief="Particle density");
        rho             as dens_mass    (Brief="Fluid density");
        Dp              as length               (Brief="Diameter of the spherical particle", Lower=1e-6);
        CD              as Real                 (Brief="Dimensionless drag coefficient", Lower=1e-6); # 1e-9
        Re              as Real                 (Brief="Reynolds number", Lower=1e-6); # 1e-9
        mu              as viscosity    (Brief="Viscosity", DisplayUnit='kg/m/s');
        
        
        EQUATIONS
        "Force balance"
        vt = sqrt(4*g*(rho_p - rho)*Dp/(3*CD*rho));
        
        "Reynolds number"
        Re = (Dp*vt*rho)/mu;


        if Re < 0.1 then
        "Drag coefficient"
                CD = 24/Re; # Re < 0.1
                else if Re <= 1e3 then
                "Drag coefficient"
                        CD = (24/Re)*(1 + 0.14*Re^0.7); # 0.1 =< Re =< 1000
                        else if Re <= 3.5e5 then
                        "Drag coefficient"
                                CD = 0.44; # 1000 < Re =< 3.5e5
                        else
                        "Drag coefficient"
                                CD = 0.19 - 8e4/Re; # 3.5e5 < Re
                        end
                end
        end
end


FlowSheet solution
        DEVICES
        vel             as problem;
        
#*      Hard convergence to 30*g!
        It needs to change the limits of CD and Re.
        Try to change lower limits to 1e-9.                     *#
        
#       SET
#       vel.g = 30*(9.80665*'m/s^2'); # Problem b
        
        
        SPECIFY
        vel.rho_p = 1800*'kg/m^3';
        vel.Dp = 0.208e-3*'m';
        vel.rho = 994.6*'kg/m^3'; # at 298.15*'K'
        vel.mu = 8.931e-4*'kg/m/s'; # at 298.15*'K'
        

        OPTIONS
        Dynamic = false;
end