models/solar/packed_bed_thermal_storage_tank.a4l

REQUIRE "solar/solar_types.a4l";
REQUIRE "johnpye/thermo_types.a4c";


MODEL Air_Properties(
	T WILL_BE temperature;
);
	(* Variables *)
	rho IS_A mass_density;			(* Air density *)
	Cp IS_A specific_heat_capacity; (* Constant pressure heat capacity *)

	T_dimless IS_A factor;
	rho_dimless IS_A factor;
	Cp_dimless IS_A factor;


	(* Equations *)
	T_dimless * 1{K} = T;
	rho = rho_dimless * 1{kg/m^3};
	Cp = Cp_dimless * 1{J/kg/K};

	rho_dimless * (8314.32 * T_dimless) = 1000 * 101.325 * 28.9645;
(*	rho = 1.2466 {kg/m^3}; *)

	Cp_dimless = (1 + ( 2.5e-10 * T_dimless^3 )) * 1000 ; 
(*	Cp = 1.012 {kJ/kg/K}; 	*)

METHODS
	METHOD bound_self;
		rho.lower_bound := 0 {kg/m^3};
		rho_dimless.lower_bound := 0;
		Cp.lower_bound := 0 {J/kg/K};
		Cp_dimless.lower_bound := 0;
	END bound_self;
END Air_Properties;


MODEL test_Air_Properties;
	T IS_A temperature;
	instance IS_A Air_Properties (T);

METHODS
	METHOD specify;
		FIX T;
	END specify;

	METHOD values;
		T := 25{K} + 273.15{K};
	END values;

	METHOD on_load;
		RUN specify;
		RUN values;
	
		RUN instance.bound_self;
	END on_load;
END test_Air_Properties;


MODEL layer;
	e IS_A real_constant;
	e :== 2.718;

	(* Variables *)
	T_f_after IS_A temperature;
	T_f_before IS_A temperature;

	T_b IS_A temperature;	
	NTU_by_N IS_A factor;

	(* Equations *)
	(T_f_after - T_b) * e^NTU_by_N = T_f_before - T_b;
END layer;


MODEL packed_bed_tank;	
	(* Constants *)	
	NL IS_A integer_constant;
	NL :== 3;
	e IS_A real_constant;
	e :== 2.718;

	(* Variables *)
	T_amb IS_A temperature;
	T_in IS_A temperature;	
	V IS_A speed; 				(* Fluid velocity *)
	D IS_A distance;			(* diameter of pebbles *)
	A IS_A area; 				(* Cross sectional area of bed [input] *)
	L IS_A distance; 			(* length of bed [input] *)
	delta_t IS_A time; 				(* process starts from zero (Input: 0 to 5hrs) *)
	epsilon IS_A fraction; 		(* bed void fraction (input) *)

	Tavg IS_A temperature;	
	T_out IS_A temperature;	
	NTU IS_A factor;
	hv IS_A volumetric_heat_transfer_coefficient; 			(* volumetric heat transfer coefficient *)
	G_dimless IS_A factor;
	D_dimless IS_A factor;
	mdot IS_A mass_rate;
	NTU_by_N IS_A factor;
	delta_x IS_A distance;
	delta_theta IS_A time;


	(* parts *)
	air_props IS_A Air_Properties (Tavg);	
	bed[1..NL] IS_A layer;

	(* Interconnections *)
	bed[1].T_f_before, T_in ARE_THE_SAME;
	bed[NL].T_f_after, T_out ARE_THE_SAME;
	NTU_by_N, bed[1..NL].NTU_by_N ARE_THE_SAME;
	FOR i IN [2..NL] CREATE
		bed[i-1].T_f_after, bed[i].T_f_before ARE_THE_SAME;
	END FOR;


	(* Equations *)
	Tavg = (T_in + T_out)/2;
	NTU * (mdot * air_props.Cp) = hv * A * L;

	hv * (D_dimless^0.7) = 650 * (G_dimless^0.7);	

	D_dimless = D / 1{m};
	G_dimless = V * air_props.rho / 1{kg/m^2/s};
	mdot = air_props.rho * V * A;
	
	delta_x = L / NL;
	NTU_by_N = NTU / NL;

	delta_theta * (air_props.rho * air_props.Cp) *  (1-epsilon) * A * L = delta_t * mdot * air_props.Cp;

	(bed[1].T_b - T_amb) * e^NTU_by_N = delta_theta * NL * (T_in - (T_amb + bed[1].T_b)/2);
	FOR i IN [2..NL] CREATE		
		(bed[i].T_b - bed[i-1].T_b) * e^NTU_by_N = delta_theta * NL * (bed[i-1].T_f_after - (bed[i-1].T_b + bed[i].T_b)/2);
    END FOR;

    
METHODS
	METHOD specify;
		FIX	T_amb, T_in, V, D, A, L, delta_t, epsilon;
	END specify;

	METHOD bound_self;
		RUN air_props.bound_self;
		G_dimless.lower_bound := 0;
		mdot.lower_bound := 0{kg/s};
		NTU.lower_bound := 0;
		NTU_by_N.lower_bound := 0;
		hv.lower_bound := 0{watt/m^3/K};
		delta_theta.lower_bound := 0 {s};
		NTU_by_N.upper_bound := 100;
	END bound_self;

	METHOD values;
		T_amb := 10 {K} + 273.15 {K};
		T_in := 40 {K} + 273.15 {K};
		V := 0.053 {m/s};
		D := 0.0125 {m};
		A := 14.8 {m^2};
		L := 1.8 {m};
		delta_t := 1 {hr};
		epsilon := 0.47;
	END values;

	METHOD default_self;
		G_dimless := 0.0638;
		NTU := 57;
		hv := 2030{watt/m^3/K};
		T_out := 20 {K} + 273.15 {K};
	END default_self;

	METHOD on_load;
		RUN specify;
		RUN bound_self;
		RUN default_self;
		RUN values;

		SOLVER QRSlv;
		OPTION convopt 'RELNOM_SCALE';
		OPTION iterationlimit 100;
	END on_load;
END packed_bed_tank;


MODEL example_packed_bed_tank REFINES packed_bed_tank;

	METHODS
		METHOD specify;
			RUN packed_bed_tank::specify;
		END specify;

		METHOD values;
			T_amb := 10 {K} + 273.15 {K};
			T_in := 40 {K} + 273.15 {K};
			V := 0.053 {m/s};
			D := 0.0125 {m};
			A := 14.8 {m^2};
			L := 1.8 {m};
			delta_t := 1 {hr};
			epsilon := 0.47;
		END values;

		METHOD on_load;
			RUN packed_bed_tank::specify;
			RUN packed_bed_tank::bound_self;
			RUN packed_bed_tank::default_self;
			RUN values;

			SOLVER QRSlv;
			OPTION convopt 'RELNOM_SCALE';
			OPTION iterationlimit 100;
		END on_load;
	
END example_packed_bed_tank;
1	REQUIRE "solar/solar_types.a4l";
2	REQUIRE "johnpye/thermo_types.a4c";
3
4
5	MODEL Air_Properties(
6	T WILL_BE temperature;
7	);
8	(* Variables *)
9	rho IS_A mass_density; (* Air density *)
10	Cp IS_A specific_heat_capacity; (* Constant pressure heat capacity *)
11
12	T_dimless IS_A factor;
13	rho_dimless IS_A factor;
14	Cp_dimless IS_A factor;
15
16
17	(* Equations *)
18	T_dimless * 1{K} = T;
19	rho = rho_dimless * 1{kg/m^3};
20	Cp = Cp_dimless * 1{J/kg/K};
21
22	rho_dimless * (8314.32 * T_dimless) = 1000 * 101.325 * 28.9645;
23	(* rho = 1.2466 {kg/m^3}; *)
24
25	Cp_dimless = (1 + ( 2.5e-10 * T_dimless^3 )) * 1000 ;
26	(* Cp = 1.012 {kJ/kg/K}; *)
27
28	METHODS
29	METHOD bound_self;
30	rho.lower_bound := 0 {kg/m^3};
31	rho_dimless.lower_bound := 0;
32	Cp.lower_bound := 0 {J/kg/K};
33	Cp_dimless.lower_bound := 0;
34	END bound_self;
35	END Air_Properties;
36
37
38	MODEL test_Air_Properties;
39	T IS_A temperature;
40	instance IS_A Air_Properties (T);
41
42	METHODS
43	METHOD specify;
44	FIX T;
45	END specify;
46
47	METHOD values;
48	T := 25{K} + 273.15{K};
49	END values;
50
51	METHOD on_load;
52	RUN specify;
53	RUN values;
54
55	RUN instance.bound_self;
56	END on_load;
57	END test_Air_Properties;
58
59
60	MODEL layer;
61	e IS_A real_constant;
62	e :== 2.718;
63
64	(* Variables *)
65	T_f_after IS_A temperature;
66	T_f_before IS_A temperature;
67
68	T_b IS_A temperature;
69	NTU_by_N IS_A factor;
70
71	(* Equations *)
72	(T_f_after - T_b) * e^NTU_by_N = T_f_before - T_b;
73	END layer;
74
75
76	MODEL packed_bed_tank;
77	(* Constants *)
78	NL IS_A integer_constant;
79	NL :== 3;
80	e IS_A real_constant;
81	e :== 2.718;
82
83	(* Variables *)
84	T_amb IS_A temperature;
85	T_in IS_A temperature;
86	V IS_A speed; (* Fluid velocity *)
87	D IS_A distance; (* diameter of pebbles *)
88	A IS_A area; (* Cross sectional area of bed [input] *)
89	L IS_A distance; (* length of bed [input] *)
90	delta_t IS_A time; (* process starts from zero (Input: 0 to 5hrs) *)
91	epsilon IS_A fraction; (* bed void fraction (input) *)
92
93	Tavg IS_A temperature;
94	T_out IS_A temperature;
95	NTU IS_A factor;
96	hv IS_A volumetric_heat_transfer_coefficient; (* volumetric heat transfer coefficient *)
97	G_dimless IS_A factor;
98	D_dimless IS_A factor;
99	mdot IS_A mass_rate;
100	NTU_by_N IS_A factor;
101	delta_x IS_A distance;
102	delta_theta IS_A time;
103
104
105	(* parts *)
106	air_props IS_A Air_Properties (Tavg);
107	bed[1..NL] IS_A layer;
108
109	(* Interconnections *)
110	bed[1].T_f_before, T_in ARE_THE_SAME;
111	bed[NL].T_f_after, T_out ARE_THE_SAME;
112	NTU_by_N, bed[1..NL].NTU_by_N ARE_THE_SAME;
113	FOR i IN [2..NL] CREATE
114	bed[i-1].T_f_after, bed[i].T_f_before ARE_THE_SAME;
115	END FOR;
116
117
118	(* Equations *)
119	Tavg = (T_in + T_out)/2;
120	NTU * (mdot * air_props.Cp) = hv * A * L;
121
122	hv * (D_dimless^0.7) = 650 * (G_dimless^0.7);
123
124	D_dimless = D / 1{m};
125	G_dimless = V * air_props.rho / 1{kg/m^2/s};
126	mdot = air_props.rho * V * A;
127
128	delta_x = L / NL;
129	NTU_by_N = NTU / NL;
130
131	delta_theta * (air_props.rho * air_props.Cp) * (1-epsilon) * A * L = delta_t * mdot * air_props.Cp;
132
133	(bed[1].T_b - T_amb) * e^NTU_by_N = delta_theta * NL * (T_in - (T_amb + bed[1].T_b)/2);
134	FOR i IN [2..NL] CREATE
135	(bed[i].T_b - bed[i-1].T_b) * e^NTU_by_N = delta_theta * NL * (bed[i-1].T_f_after - (bed[i-1].T_b + bed[i].T_b)/2);
136	END FOR;
137
138
139	METHODS
140	METHOD specify;
141	FIX T_amb, T_in, V, D, A, L, delta_t, epsilon;
142	END specify;
143
144	METHOD bound_self;
145	RUN air_props.bound_self;
146	G_dimless.lower_bound := 0;
147	mdot.lower_bound := 0{kg/s};
148	NTU.lower_bound := 0;
149	NTU_by_N.lower_bound := 0;
150	hv.lower_bound := 0{watt/m^3/K};
151	delta_theta.lower_bound := 0 {s};
152	NTU_by_N.upper_bound := 100;
153	END bound_self;
154
155	METHOD values;
156	T_amb := 10 {K} + 273.15 {K};
157	T_in := 40 {K} + 273.15 {K};
158	V := 0.053 {m/s};
159	D := 0.0125 {m};
160	A := 14.8 {m^2};
161	L := 1.8 {m};
162	delta_t := 1 {hr};
163	epsilon := 0.47;
164	END values;
165
166	METHOD default_self;
167	G_dimless := 0.0638;
168	NTU := 57;
169	hv := 2030{watt/m^3/K};
170	T_out := 20 {K} + 273.15 {K};
171	END default_self;
172
173	METHOD on_load;
174	RUN specify;
175	RUN bound_self;
176	RUN default_self;
177	RUN values;
178
179	SOLVER QRSlv;
180	OPTION convopt 'RELNOM_SCALE';
181	OPTION iterationlimit 100;
182	END on_load;
183	END packed_bed_tank;
184
185
186	MODEL example_packed_bed_tank REFINES packed_bed_tank;
187
188	METHODS
189	METHOD specify;
190	RUN packed_bed_tank::specify;
191	END specify;
192
193	METHOD values;
194	T_amb := 10 {K} + 273.15 {K};
195	T_in := 40 {K} + 273.15 {K};
196	V := 0.053 {m/s};
197	D := 0.0125 {m};
198	A := 14.8 {m^2};
199	L := 1.8 {m};
200	delta_t := 1 {hr};
201	epsilon := 0.47;
202	END values;
203
204	METHOD on_load;
205	RUN packed_bed_tank::specify;
206	RUN packed_bed_tank::bound_self;
207	RUN packed_bed_tank::default_self;
208	RUN values;
209
210	SOLVER QRSlv;
211	OPTION convopt 'RELNOM_SCALE';
212	OPTION iterationlimit 100;
213	END on_load;
214
215	END example_packed_bed_tank;