source: trunk/sample/miscellaneous/tenprobs/prob05.mso

Last change on this file was 228, checked in by Rodolfo Rodrigues, 15 years ago

Add more detailed header

File size: 3.2 KB
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1#*---------------------------------------------------------------------
2* EMSO Model Library (EML) Copyright (C) 2004 - 2007 ALSOC.
3*
4* This LIBRARY is free software; you can distribute it and/or modify
5* it under the therms of the ALSOC FREE LICENSE as available at
6* http://www.enq.ufrgs.br/alsoc.
7*
8* EMSO Copyright (C) 2004 - 2007 ALSOC, original code
9* from http://www.rps.eng.br Copyright (C) 2002-2004.
10* All rights reserved.
11*
12* EMSO is distributed under the therms of the ALSOC LICENSE as
13* available at http://www.enq.ufrgs.br/alsoc.
14*
15*----------------------------------------------------------------------
16* 5. Terminal velocity of falling particles
17*----------------------------------------------------------------------
18*
19*   Description:
20*      This problem is part of a collection of 10 representative
21*       problems in Chemical Engineering for solution by numerical methods
22*       developed for Cutlip (1998).
23*
24*   Subject:
25*       * Fluid Dynamics
26*
27*       Concepts utilized:
28*               Calculation of terminal velocity of solid particles falling in
29*       fluids under the force of gravity.
30*
31*       Numerical method:
32*               * Single nonlinear algebraic equation
33*
34*   Reference:
35*       * CUTLIP et al. A collection of 10 numerical problems in
36*       chemical engineering solved by various mathematical software
37*       packages. Comp. Appl. in Eng. Education. v. 6, 169-180, 1998.
38*       * More informations and a detailed description of all problems
39*       is available online in http://www.polymath-software.com/ASEE
40*
41*----------------------------------------------------------------------
42* Author: Rodolfo Rodrigues
43* GIMSCOP/UFRGS - Group of Integration, Modeling, Simulation,
44*                                       Control, and Optimization of Processes
45* $Id$
46*--------------------------------------------------------------------*#
47using "types";
48
49
50
51Model problem
52        PARAMETERS
53        g               as acceleration (Brief="Accelaration of gravity", Default=9.80665);
54       
55       
56        VARIABLES
57        vt              as velocity             (Brief="Terminal velocity");
58        rho_p   as dens_mass    (Brief="Particle density");
59        rho             as dens_mass    (Brief="Fluid density");
60        Dp              as length               (Brief="Diameter of the spherical particle", Lower=1e-6);
61        CD              as Real                 (Brief="Dimensionless drag coefficient", Lower=1e-6); # 1e-9
62        Re              as Real                 (Brief="Reynolds number", Lower=1e-6); # 1e-9
63        mu              as viscosity    (Brief="Viscosity", DisplayUnit='kg/m/s');
64       
65       
66        EQUATIONS
67        "Force balance"
68        vt = sqrt(4*g*(rho_p - rho)*Dp/(3*CD*rho));
69       
70        "Reynolds number"
71        Re = (Dp*vt*rho)/mu;
72
73
74        if Re < 0.1 then
75        "Drag coefficient"
76                CD = 24/Re; # Re < 0.1
77                else if Re <= 1e3 then
78                "Drag coefficient"
79                        CD = (24/Re)*(1 + 0.14*Re^0.7); # 0.1 =< Re =< 1000
80                        else if Re <= 3.5e5 then
81                        "Drag coefficient"
82                                CD = 0.44; # 1000 < Re =< 3.5e5
83                        else
84                        "Drag coefficient"
85                                CD = 0.19 - 8e4/Re; # 3.5e5 < Re
86                        end
87                end
88        end
89end
90
91
92FlowSheet solution
93        DEVICES
94        vel             as problem;
95       
96#*      Hard convergence to 30*g!
97        It needs to change the limits of CD and Re.
98        Try to change lower limits to 1e-9.                     *#
99       
100#       SET
101#       vel.g = 30*(9.80665*'m/s^2'); # Problem b
102       
103       
104        SPECIFY
105        vel.rho_p = 1800*'kg/m^3';
106        vel.Dp = 0.208e-3*'m';
107        vel.rho = 994.6*'kg/m^3'; # at 298.15*'K'
108        vel.mu = 8.931e-4*'kg/m/s'; # at 298.15*'K'
109       
110
111        OPTIONS
112        Dynamic = false;
113end
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