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, see <http://www.gnu.org/licenses/>.
*)(**
	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	johnpye	611	(* 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	jpye	2649	You should have received a copy of the GNU General Public License
17			along with this program. If not, see <http://www.gnu.org/licenses/>.
18	johnpye	611	)(*
19			This is a simple model for computing the
20			steady-state temperature and heat loss profile
21			of a multi-layered pipe-plus-insulation
22
23			by John Pye
24			*)
25
26			REQUIRE "atoms.a4l";
27			REQUIRE "johnpye/thermo_types.a4c";
28
29			MODEL radial_loss;
30			D_1 IS_A distance;
31			D_2 IS_A distance;
32			q IS_A energy_rate;
33			L IS_A distance;
34			T_1, T_2 IS_A temperature;
35			METHODS
36			METHOD specify;
37			FIX D_1, D_2;
38			END specify;
39			END radial_loss;
40
41			(*
42			Wall conduction
43			*)
44			MODEL wall_conduction REFINES radial_loss;
45			k IS_A thermal_conductivity;
46
47	johnpye	617	q = 2 * 1{PI} * L * k * (T_1 - T_2) / ln(D_2/D_1);
48	johnpye	611
49			END wall_conduction;
50
51			(*
52			Convection boundary
53			*)
54			MODEL convection_boundary REFINES radial_loss;
55			h IS_A heat_transfer_coefficient;
56			D_1, D_2 ARE_THE_SAME;
57	johnpye	617
58			(* heat loss is positive if T_1 > T_2 *)
59	johnpye	611	q = h * 1{PI} * D_1 * (T_1 - T_2);
60
61			END convection_boundary;
62	johnpye	612
63	johnpye	617	(**
64			This modes a thick pipe with internal flow, surrounded by 100mm of
65			insulation and a thin external metal shell. In other words, a fairly
66			typical lagged high-temperature pipe as used in power and chemical plant
67			applications.
68
69			Solve the model, then examine the values of T_1 and T_2 for each layer.
70
71			@TODO add ability to plot the temperature versus radial distance...
72			*)
73	johnpye	612	MODEL pipe_test REFINES radial_loss;
74
75			n IS_A integer_constant;
76			n:==5;
77
78	johnpye	617	U IS_A heat_transfer_coefficient;
79			q = U * (1{PI} * D_1) * (loss[1].T_2 - T_2);
80
81	johnpye	612	loss[1..5] IS_A radial_loss;
82
83			loss[1] IS_REFINED_TO convection_boundary;
84			loss[2] IS_REFINED_TO wall_conduction;
85			loss[3] IS_REFINED_TO wall_conduction;
86			loss[4] IS_REFINED_TO wall_conduction;
87			loss[5] IS_REFINED_TO convection_boundary;
88
89			L, loss[1..5].L ARE_THE_SAME;
90
91	johnpye	615	FOR i IN [2..n] CREATE
92	johnpye	611	(* layers are touching *)
93			loss[i].D_1, loss[i-1].D_2 ARE_THE_SAME;
94	johnpye	612
95			(* steady state: heat rate is uniform *)
96	johnpye	615	loss[i].q,loss[i-1].q ARE_THE_SAME;
97
98	johnpye	616	loss[i].T_1, loss[i-1].T_2 ARE_THE_SAME;
99
100	johnpye	612	END FOR;
101
102	johnpye	616	loss[1].D_1, D_1 ARE_THE_SAME;
103	johnpye	615	loss[n].D_2, D_2 ARE_THE_SAME;
104
105	johnpye	616	loss[1].T_1, T_1 ARE_THE_SAME;
106			loss[n].T_2, T_2 ARE_THE_SAME;
107	johnpye	615
108	johnpye	616	loss[1].q, q ARE_THE_SAME;
109	johnpye	615
110	johnpye	612	METHODS
111			METHOD default_self;
112			RUN reset; RUN values;
113			END default_self;
114	johnpye	611
115			METHOD specify;
116			FIX loss[1].h;
117			FIX loss[2..4].k;
118	johnpye	616	FIX loss[5].h;
119			FIX L;
120			FIX T_1, T_2;
121	johnpye	611
122	johnpye	615	FIX loss[2].D_1, loss[2].D_2;
123			FIX loss[4].D_1, loss[4].D_2;
124	johnpye	611	END specify;
125
126	johnpye	615	METHOD values;
127	johnpye	616	L := 1 {m};
128			T_1 := 250 {K} + 273.15 {K};
129			T_2 := 25 {K} + 273.15 {K};
130	johnpye	615
131	johnpye	611	loss[1].h := 1000 {W/m^2/K};
132			loss[2].k := 40 {W/m/K}; (* 'alloy steel', Ashby & Jones, Eng Matls 2, p.11 *)
133			loss[3].k := 0.05 {W/m/K}; (* Masud's figure for lagging *)
134			loss[4].k := 240 {W/m/K}; (* aluminium, Ashby & Jones, Eng Matls 2, p.11 *)
135			loss[5].h := 50 {W/m^2/K};
136
137	johnpye	617	loss[2].D_1 := 0.05 {m}; (* pipe interior *)
138			loss[2].D_2 := 0.07 {m}; (* pipe exterior *)
139	johnpye	611	loss[4].D_1 := 0.17 {m}; (* cover interior *)
140			loss[4].D_2 := 0.19 {m}; (* cover exterior *)
141			END values;
142	johnpye	612	END pipe_test;