trunk/models/sonic.a4c

REQUIRE "atoms.a4l";
(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
PROVIDE "sonic.a4c";
(*
 * This file is part of the ASCEND Modeling Library and is released
 * under the GNU Public License as described at the end of this file.
 *
 * Use of this module is demonstrated by the associated script file
 * sonic.a4s.
 *)

(*
   Ascend model of the Adiabatic compressible flow  example presented by
Zaher -- Conditional Modeling. Ph.D. Thesis, Carnegie Mellon University,
Pittsburgh, PA, 15213. 1995 --. The problem represents the flow of a
compressible gas in a circular pipe of constant diameter. There is a
disjunctive statement which represents whether the flow is sonic or
subsonic. It represent a problem which we can represent as a conditional
model and  solve  with the ascend conditional solver CMSlv.

This model requires:
			"system.a4l"
		    	"atoms.a4l"
*)

(* ************************************************* *)

MODEL sonic;

	Pi 		IS_A pressure;
	Pf  		IS_A pressure;
	Pd  		IS_A pressure;
	Ti  		IS_A temperature;
	Tf 		IS_A temperature;
	Mi 		IS_A fraction;
	Mf  		IS_A fraction;
	D  		IS_A distance;
	F 		IS_A molar_rate;
	friction  	IS_A factor;
	gamma 		IS_A factor;
	mw 		IS_A molar_mass;
	L       	IS_A distance;
	R		IS_A gas_constant;
	Pifac           IS_A factor;
        sonic_flow	IS_A boolean_var;

(* boundary *)
        CONDITIONAL
          cond: (Pd - Pf) * 1.0 {atm^-1} <= Mf - 1.0;
	END CONDITIONAL;

        sonic_flow == SATISFIED(cond,1e-08);

(* Variant Equations *)

	not_sonic: Pf = Pd;
	sonic: Mf = 1.0;

(* Disjunctive statement *)

        WHEN (sonic_flow)
          CASE TRUE:
		USE sonic;
          CASE FALSE:
		USE not_sonic;
	END WHEN;

(* Invariant Equations *)

	R * F * Ti / Pi = Pifac * (D^2) * Mi/4.0 * (gamma * R *Ti/mw)^(1/2);
	R * F * Tf / Pf = Pifac * (D^2) * Mf/4.0 * (gamma * R *Tf/mw)^(1/2);
	Tf/Ti = (1 + 0.5*(gamma-1)*(Mi^2))/(1 + 0.5*(gamma-1)*(Mf^2));

        1/(Mi^2) - 1/(Mf^2) - 4*gamma*friction*L/D = 0.5*(gamma+1)*
	                         ln( ((Mf^2)*(1 + 0.5*(gamma-1)*(Mi^2)))/
	                             ((Mi^2)*(1 + 0.5*(gamma-1)*(Mf^2)))  );

  METHODS

    METHOD default_self;
    END default_self;

    METHOD specify;
	friction.fixed := TRUE;
	gamma.fixed := TRUE;
	mw.fixed := TRUE;
	L.fixed := TRUE;
	Ti.fixed := TRUE;
	Pi.fixed := TRUE;
	Pd.fixed := TRUE;
	D.fixed := TRUE;
	Pifac.fixed := TRUE;
    END specify;

    METHOD values;
        (* fixed values*)
	friction := 0.01;
	gamma := 1.292;
	mw := 16 {g/g_mole};
	L := 1 {m};
	Ti := 300.0 {K};
	Pi := 10.0 {atm};
	Pd := 5.0 {atm};
	D :=  5.0 {cm};      (* boundary is 4.08844 {cm} *)
	Pifac := 3.14159;
        (* initial values *)
	Mi := 0.5;
	Mf := 0.5;
	Tf := 300.0 {K};
	Pf := 5.0 {atm};
	F  := 200.0 {g_mole/s};

        (* initial boolean value *)
        sonic_flow := SATISFIED(cond,1e-08);
    END values;

END sonic;


(*
 *  sonic.a4c
 *  by Vicente Rico-Ramirez
 *  April 10, 1998
 *  Part of the ASCEND Library
 *  $Date: 1998/06/17 19:15:06 $
 *  $Revision: 1.3 $
 *  $Author: mthomas $
 *  $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/sonic.a4c,v $
 *
 *  This file is part of the ASCEND Modeling Library.
 *
 *  Copyright (C) 1998 Carnegie Mellon University
 *
 *  The ASCEND Modeling Library is free software; you can redistribute
 *  it and/or modify it under the terms of the GNU General Public
 *  License as published by the Free Software Foundation; either
 *  version 2 of the License, or (at your option) any later version.
 *
 *  The ASCEND Modeling Library is distributed in hope that it will be
 *  useful, but WITHOUT ANY WARRANTY; without even the implied
 *  warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *  See the GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with the program; if not, write to the Free Software
 *  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA.  Check
 *  the file named COPYING.
 *)
1	REQUIRE "atoms.a4l";
2	(* => atoms.a4l, measures.a4l, system.a4l, basemodel.a4l *)
3	PROVIDE "sonic.a4c";
4	(*
5	* This file is part of the ASCEND Modeling Library and is released
6	* under the GNU Public License as described at the end of this file.
7	*
8	* Use of this module is demonstrated by the associated script file
9	* sonic.a4s.
10	*)
11
12	(*
13	Ascend model of the Adiabatic compressible flow example presented by
14	Zaher -- Conditional Modeling. Ph.D. Thesis, Carnegie Mellon University,
15	Pittsburgh, PA, 15213. 1995 --. The problem represents the flow of a
16	compressible gas in a circular pipe of constant diameter. There is a
17	disjunctive statement which represents whether the flow is sonic or
18	subsonic. It represent a problem which we can represent as a conditional
19	model and solve with the ascend conditional solver CMSlv.
20
21	This model requires:
22	"system.a4l"
23	"atoms.a4l"
24	*)
25
26	(* ************************************************* *)
27
28	MODEL sonic;
29
30	Pi IS_A pressure;
31	Pf IS_A pressure;
32	Pd IS_A pressure;
33	Ti IS_A temperature;
34	Tf IS_A temperature;
35	Mi IS_A fraction;
36	Mf IS_A fraction;
37	D IS_A distance;
38	F IS_A molar_rate;
39	friction IS_A factor;
40	gamma IS_A factor;
41	mw IS_A molar_mass;
42	L IS_A distance;
43	R IS_A gas_constant;
44	Pifac IS_A factor;
45	sonic_flow IS_A boolean_var;
46
47	(* boundary *)
48	CONDITIONAL
49	cond: (Pd - Pf) * 1.0 {atm^-1} <= Mf - 1.0;
50	END CONDITIONAL;
51
52	sonic_flow == SATISFIED(cond,1e-08);
53
54	(* Variant Equations *)
55
56	not_sonic: Pf = Pd;
57	sonic: Mf = 1.0;
58
59	(* Disjunctive statement *)
60
61	WHEN (sonic_flow)
62	CASE TRUE:
63	USE sonic;
64	CASE FALSE:
65	USE not_sonic;
66	END WHEN;
67
68	(* Invariant Equations *)
69
70	R * F * Ti / Pi = Pifac * (D^2) * Mi/4.0 * (gamma * R *Ti/mw)^(1/2);
71	R * F * Tf / Pf = Pifac * (D^2) * Mf/4.0 * (gamma * R *Tf/mw)^(1/2);
72	Tf/Ti = (1 + 0.5(gamma-1)(Mi^2))/(1 + 0.5(gamma-1)(Mf^2));
73
74	1/(Mi^2) - 1/(Mf^2) - 4gammafrictionL/D = 0.5(gamma+1)*
75	ln( ((Mf^2)(1 + 0.5(gamma-1)*(Mi^2)))/
76	((Mi^2)(1 + 0.5(gamma-1)*(Mf^2))) );
77
78	METHODS
79
80	METHOD default_self;
81	END default_self;
82
83	METHOD specify;
84	friction.fixed := TRUE;
85	gamma.fixed := TRUE;
86	mw.fixed := TRUE;
87	L.fixed := TRUE;
88	Ti.fixed := TRUE;
89	Pi.fixed := TRUE;
90	Pd.fixed := TRUE;
91	D.fixed := TRUE;
92	Pifac.fixed := TRUE;
93	END specify;
94
95	METHOD values;
96	(* fixed values*)
97	friction := 0.01;
98	gamma := 1.292;
99	mw := 16 {g/g_mole};
100	L := 1 {m};
101	Ti := 300.0 {K};
102	Pi := 10.0 {atm};
103	Pd := 5.0 {atm};
104	D := 5.0 {cm}; (* boundary is 4.08844 {cm} *)
105	Pifac := 3.14159;
106	(* initial values *)
107	Mi := 0.5;
108	Mf := 0.5;
109	Tf := 300.0 {K};
110	Pf := 5.0 {atm};
111	F := 200.0 {g_mole/s};
112
113	(* initial boolean value *)
114	sonic_flow := SATISFIED(cond,1e-08);
115	END values;
116
117	END sonic;
118
119
120	(*
121	* sonic.a4c
122	* by Vicente Rico-Ramirez
123	* April 10, 1998
124	* Part of the ASCEND Library
125	* $Date: 1998/06/17 19:15:06 $
126	* $Revision: 1.3 $
127	* $Author: mthomas $
128	* $Source: /afs/cs.cmu.edu/project/ascend/Repository/models/sonic.a4c,v $
129	*
130	* This file is part of the ASCEND Modeling Library.
131	*
132	* Copyright (C) 1998 Carnegie Mellon University
133	*
134	* The ASCEND Modeling Library is free software; you can redistribute
135	* it and/or modify it under the terms of the GNU General Public
136	* License as published by the Free Software Foundation; either
137	* version 2 of the License, or (at your option) any later version.
138	*
139	* The ASCEND Modeling Library is distributed in hope that it will be
140	* useful, but WITHOUT ANY WARRANTY; without even the implied
141	* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
142	* See the GNU General Public License for more details.
143	*
144	* You should have received a copy of the GNU General Public License
145	* along with the program; if not, write to the Free Software
146	* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check
147	* the file named COPYING.
148	*)