models/johnpye/radialheatloss.a4c

(*	ASCEND model library
	Copyright (c) 2006 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 of the License, 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, write to the Free
	Software Foundation, Inc., 59 Temple Place, Suite 330,
	Boston, MA 02111-1307  USA
*)(**
	This is a simple model for computing the
	steady-state temperature and heat loss profile 
	of a multi-layered pipe-plus-insulation
	
	by John Pye
*)

REQUIRE "atoms.a4l";
REQUIRE "johnpye/thermo_types.a4c";

MODEL radial_loss;
	D_1 IS_A distance;
	D_2 IS_A distance;
	q IS_A energy_rate;
	L IS_A distance;
	T_1, T_2 IS_A temperature;
METHODS
METHOD specify;
	FIX D_1, D_2;
END specify;
END radial_loss;

(*
	Wall conduction
*)
MODEL wall_conduction REFINES radial_loss;
	k IS_A thermal_conductivity;
	
	q = 2 * 1{PI} * L * k * (T_1 - T_2) / ln(D_2/D_1);

END wall_conduction;

(*
	Convection boundary
*)
MODEL convection_boundary REFINES radial_loss;
	h IS_A heat_transfer_coefficient;
	D_1, D_2 ARE_THE_SAME;
	
	(* heat loss is positive if T_1 > T_2 *)
	q = h * 1{PI} * D_1 * (T_1 - T_2);

END convection_boundary;

(**
	This modes a thick pipe with internal flow, surrounded by 100mm of
	insulation and a thin external metal shell. In other words, a fairly
	typical lagged high-temperature pipe as used in power and chemical plant
	applications.

	Solve the model, then examine the values of T_1 and T_2 for each layer.

	@TODO add ability to plot the temperature versus radial distance...
*)
MODEL pipe_test REFINES radial_loss;

	n IS_A integer_constant;
	n:==5;

	U IS_A heat_transfer_coefficient;
	q = U * (1{PI} * D_1) * (loss[1].T_2 - T_2);
	
	loss[1..5] IS_A radial_loss;

	loss[1] IS_REFINED_TO convection_boundary;
	loss[2] IS_REFINED_TO wall_conduction;
	loss[3] IS_REFINED_TO wall_conduction;
	loss[4] IS_REFINED_TO wall_conduction;
	loss[5] IS_REFINED_TO convection_boundary;

	L, loss[1..5].L ARE_THE_SAME;
	
	FOR i IN [2..n] CREATE
		(* layers are touching *)
		loss[i].D_1, loss[i-1].D_2 ARE_THE_SAME;

		(* steady state: heat rate is uniform *)
		loss[i].q,loss[i-1].q ARE_THE_SAME;

		loss[i].T_1, loss[i-1].T_2 ARE_THE_SAME;

	END FOR;

	loss[1].D_1, D_1 ARE_THE_SAME;
	loss[n].D_2, D_2 ARE_THE_SAME;

	loss[1].T_1, T_1 ARE_THE_SAME;
	loss[n].T_2, T_2 ARE_THE_SAME;

	loss[1].q, q ARE_THE_SAME;

METHODS
METHOD default_self;
	RUN reset; RUN values;
END default_self;

METHOD specify;
	FIX loss[1].h;
	FIX loss[2..4].k;
	FIX loss[5].h;
	FIX L;
	FIX T_1, T_2;
	
	FIX loss[2].D_1, loss[2].D_2;
	FIX loss[4].D_1, loss[4].D_2;
END specify;

METHOD values;
	L := 1 {m};
	T_1 := 250 {K} + 273.15 {K};
	T_2 := 25 {K} + 273.15 {K};

	loss[1].h := 1000 {W/m^2/K};
	loss[2].k := 40 {W/m/K}; (* 'alloy steel', Ashby & Jones, Eng Matls 2, p.11 *)
	loss[3].k := 0.05 {W/m/K}; (* Masud's figure for lagging *)
	loss[4].k := 240 {W/m/K}; (* aluminium, Ashby & Jones, Eng Matls 2, p.11 *)
	loss[5].h := 50 {W/m^2/K};
	
	loss[2].D_1 := 0.05 {m}; (* pipe interior *)
	loss[2].D_2 := 0.07 {m}; (* pipe exterior *)
	loss[4].D_1 := 0.17 {m}; (* cover interior *)
	loss[4].D_2 := 0.19 {m}; (* cover exterior *)
END values;
END pipe_test;
1	(* ASCEND model library
2	Copyright (c) 2006 Carnegie Mellon University
3
4	This program is free software; you can redistribute it
5	and/or modify it under the terms of the GNU General Public
6	License as published by the Free Software Foundation; either
7	version 2 of the License, or (at your option) any later
8	version.
9
10	This program is distributed in the hope that it will be
11	useful, but WITHOUT ANY WARRANTY; without even the implied
12	warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
13	PURPOSE. See the GNU General Public License for more
14	details.
15
16	You should have received a copy of the GNU General Public
17	License along with this program; if not, write to the Free
18	Software Foundation, Inc., 59 Temple Place, Suite 330,
19	Boston, MA 02111-1307 USA
20	)(*
21	This is a simple model for computing the
22	steady-state temperature and heat loss profile
23	of a multi-layered pipe-plus-insulation
24
25	by John Pye
26	*)
27
28	REQUIRE "atoms.a4l";
29	REQUIRE "johnpye/thermo_types.a4c";
30
31	MODEL radial_loss;
32	D_1 IS_A distance;
33	D_2 IS_A distance;
34	q IS_A energy_rate;
35	L IS_A distance;
36	T_1, T_2 IS_A temperature;
37	METHODS
38	METHOD specify;
39	FIX D_1, D_2;
40	END specify;
41	END radial_loss;
42
43	(*
44	Wall conduction
45	*)
46	MODEL wall_conduction REFINES radial_loss;
47	k IS_A thermal_conductivity;
48
49	q = 2 * 1{PI} * L * k * (T_1 - T_2) / ln(D_2/D_1);
50
51	END wall_conduction;
52
53	(*
54	Convection boundary
55	*)
56	MODEL convection_boundary REFINES radial_loss;
57	h IS_A heat_transfer_coefficient;
58	D_1, D_2 ARE_THE_SAME;
59
60	(* heat loss is positive if T_1 > T_2 *)
61	q = h * 1{PI} * D_1 * (T_1 - T_2);
62
63	END convection_boundary;
64
65	(**
66	This modes a thick pipe with internal flow, surrounded by 100mm of
67	insulation and a thin external metal shell. In other words, a fairly
68	typical lagged high-temperature pipe as used in power and chemical plant
69	applications.
70
71	Solve the model, then examine the values of T_1 and T_2 for each layer.
72
73	@TODO add ability to plot the temperature versus radial distance...
74	*)
75	MODEL pipe_test REFINES radial_loss;
76
77	n IS_A integer_constant;
78	n:==5;
79
80	U IS_A heat_transfer_coefficient;
81	q = U * (1{PI} * D_1) * (loss[1].T_2 - T_2);
82
83	loss[1..5] IS_A radial_loss;
84
85	loss[1] IS_REFINED_TO convection_boundary;
86	loss[2] IS_REFINED_TO wall_conduction;
87	loss[3] IS_REFINED_TO wall_conduction;
88	loss[4] IS_REFINED_TO wall_conduction;
89	loss[5] IS_REFINED_TO convection_boundary;
90
91	L, loss[1..5].L ARE_THE_SAME;
92
93	FOR i IN [2..n] CREATE
94	(* layers are touching *)
95	loss[i].D_1, loss[i-1].D_2 ARE_THE_SAME;
96
97	(* steady state: heat rate is uniform *)
98	loss[i].q,loss[i-1].q ARE_THE_SAME;
99
100	loss[i].T_1, loss[i-1].T_2 ARE_THE_SAME;
101
102	END FOR;
103
104	loss[1].D_1, D_1 ARE_THE_SAME;
105	loss[n].D_2, D_2 ARE_THE_SAME;
106
107	loss[1].T_1, T_1 ARE_THE_SAME;
108	loss[n].T_2, T_2 ARE_THE_SAME;
109
110	loss[1].q, q ARE_THE_SAME;
111
112	METHODS
113	METHOD default_self;
114	RUN reset; RUN values;
115	END default_self;
116
117	METHOD specify;
118	FIX loss[1].h;
119	FIX loss[2..4].k;
120	FIX loss[5].h;
121	FIX L;
122	FIX T_1, T_2;
123
124	FIX loss[2].D_1, loss[2].D_2;
125	FIX loss[4].D_1, loss[4].D_2;
126	END specify;
127
128	METHOD values;
129	L := 1 {m};
130	T_1 := 250 {K} + 273.15 {K};
131	T_2 := 25 {K} + 273.15 {K};
132
133	loss[1].h := 1000 {W/m^2/K};
134	loss[2].k := 40 {W/m/K}; (* 'alloy steel', Ashby & Jones, Eng Matls 2, p.11 *)
135	loss[3].k := 0.05 {W/m/K}; (* Masud's figure for lagging *)
136	loss[4].k := 240 {W/m/K}; (* aluminium, Ashby & Jones, Eng Matls 2, p.11 *)
137	loss[5].h := 50 {W/m^2/K};
138
139	loss[2].D_1 := 0.05 {m}; (* pipe interior *)
140	loss[2].D_2 := 0.07 {m}; (* pipe exterior *)
141	loss[4].D_1 := 0.17 {m}; (* cover interior *)
142	loss[4].D_2 := 0.19 {m}; (* cover exterior *)
143	END values;
144	END pipe_test;