trunk/models/sonic.a4c

(*	ASCEND modelling environment
	Copyright (C) 1998, 2007 Carnegie Mellon University

	This program 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, or (at your option)
	any later version.

	This program is distributed in the 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 this program.  If not, see <http://www.gnu.org/licenses/>.
*)
REQUIRE "atoms.a4l";
(*
	Model of adiabatic compressible flow. 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. This model requires the conditional solver CMSlv.

	The problem is described in the thesis
	J Zaher, 'Conditional Modeling', Ph.D. Thesis, Carnegie Mellon University,
	Pittsburgh, PA, 15213. 1995.

	Model by Vicente Rico-Ramirez, 10 Apr 1998.

	If using the Tcl/Tk interface, see the associated script file sonic.a4s.
*)
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 molar_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;
		FIX friction;
		FIX gamma;
		FIX mw;
		FIX L;
		FIX Ti;
		FIX Pi;
		FIX Pd;
		FIX D;
		FIX Pifac;
	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;

	METHOD on_load;
		RUN default_self;
		RUN reset;
		RUN values;
	END on_load;

	METHOD self_test;
		IF D < 4.08844 {cm} THEN
			ASSERT sonic_flow == FALSE;
		ELSE
			ASSERT sonic_flow == TRUE;
		END IF;
	END self_test;

END sonic;
1	jpye	1344	(* ASCEND modelling environment
2			Copyright (C) 1998, 2007 Carnegie Mellon University
3
4			This program is free software; you can redistribute it and/or modify
5			it under the terms of the GNU General Public License as published by
6			the Free Software Foundation; either version 2, or (at your option)
7			any later version.
8
9			This program is distributed in the hope that it will be useful,
10			but WITHOUT ANY WARRANTY; without even the implied warranty of
11			MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
12			GNU General Public License for more details.
13
14			You should have received a copy of the GNU General Public License
15	jpye	2649	along with this program. If not, see <http://www.gnu.org/licenses/>.
16	jpye	1344	*)
17	aw0a	1	REQUIRE "atoms.a4l";
18			(*
19	jpye	1344	Model of adiabatic compressible flow. The problem represents the flow of a
20			compressible gas in a circular pipe of constant diameter. There is a
21			disjunctive statement which represents whether the flow is sonic or
22			subsonic. This model requires the conditional solver CMSlv.
23	aw0a	1
24	jpye	1344	The problem is described in the thesis
25			J Zaher, 'Conditional Modeling', Ph.D. Thesis, Carnegie Mellon University,
26			Pittsburgh, PA, 15213. 1995.
27	aw0a	1
28	jpye	1344	Model by Vicente Rico-Ramirez, 10 Apr 1998.
29
30			If using the Tcl/Tk interface, see the associated script file sonic.a4s.
31	aw0a	1	*)
32			MODEL sonic;
33
34	jpye	1344	Pi IS_A pressure;
35			Pf IS_A pressure;
36			Pd IS_A pressure;
37			Ti IS_A temperature;
38			Tf IS_A temperature;
39			Mi IS_A fraction;
40			Mf IS_A fraction;
41			D IS_A distance;
42			F IS_A molar_rate;
43			friction IS_A factor;
44			gamma IS_A factor;
45			mw IS_A molar_mass;
46			L IS_A distance;
47	jose	2071	R IS_A molar_gas_constant;
48	jpye	1344	Pifac IS_A factor;
49			sonic_flow IS_A boolean_var;
50	aw0a	1
51	jpye	1344	(* boundary *)
52			CONDITIONAL
53	aw0a	1	cond: (Pd - Pf) * 1.0 {atm^-1} <= Mf - 1.0;
54			END CONDITIONAL;
55
56	jpye	1344	sonic_flow == SATISFIED(cond,1e-08);
57	aw0a	1
58	jpye	1344	(* Variant Equations *)
59	aw0a	1
60			not_sonic: Pf = Pd;
61			sonic: Mf = 1.0;
62
63	jpye	1344	(* Disjunctive statement *)
64	aw0a	1
65	jpye	1344	WHEN (sonic_flow)
66			CASE TRUE:
67			USE sonic;
68			CASE FALSE:
69			USE not_sonic;
70	aw0a	1	END WHEN;
71
72	jpye	1344	(* Invariant Equations *)
73	aw0a	1
74			R * F * Ti / Pi = Pifac * (D^2) * Mi/4.0 * (gamma * R *Ti/mw)^(1/2);
75	jpye	1344
76	aw0a	1	R * F * Tf / Pf = Pifac * (D^2) * Mf/4.0 * (gamma * R *Tf/mw)^(1/2);
77	jpye	1344
78	aw0a	1	Tf/Ti = (1 + 0.5(gamma-1)(Mi^2))/(1 + 0.5(gamma-1)(Mf^2));
79
80	jpye	1344	1/(Mi^2) - 1/(Mf^2) - 4 * gamma * friction * L / D =
81			0.5 * (gamma + 1) * ln(
82			((Mf^2)(1 + 0.5(gamma-1)*(Mi^2)))
83			/ ((Mi^2)(1 + 0.5(gamma-1)*(Mf^2)))
84			);
85	aw0a	1
86	jpye	1344	METHODS
87	aw0a	1
88	jpye	1344	METHOD default_self;
89			END default_self;
90	aw0a	1
91	jpye	1344	METHOD specify;
92			FIX friction;
93			FIX gamma;
94			FIX mw;
95			FIX L;
96			FIX Ti;
97			FIX Pi;
98			FIX Pd;
99			FIX D;
100			FIX Pifac;
101			END specify;
102	aw0a	1
103	jpye	1344	METHOD values;
104			(* fixed values*)
105			friction := 0.01;
106			gamma := 1.292;
107			mw := 16 {g/g_mole};
108			L := 1 {m};
109			Ti := 300.0 {K};
110			Pi := 10.0 {atm};
111			Pd := 5.0 {atm};
112			D := 5.0 {cm}; (* boundary is 4.08844 {cm} *)
113			Pifac := 3.14159;
114	aw0a	1
115	jpye	1344	(* initial values *)
116			Mi := 0.5;
117			Mf := 0.5;
118			Tf := 300.0 {K};
119			Pf := 5.0 {atm};
120			F := 200.0 {g_mole/s};
121	aw0a	1
122	jpye	1344	(* initial boolean value *)
123			sonic_flow := SATISFIED(cond,1e-08);
124			END values;
125	aw0a	1
126	jpye	1344	METHOD on_load;
127			RUN default_self;
128			RUN reset;
129			RUN values;
130			END on_load;
131	aw0a	1
132	jpye	1344	METHOD self_test;
133			IF D < 4.08844 {cm} THEN
134			ASSERT sonic_flow == FALSE;
135			ELSE
136			ASSERT sonic_flow == TRUE;
137			END IF;
138			END self_test;
139
140			END sonic;