models/johnpye/absorber.a4c

REQUIRE "johnpye/iapws95.a4c";
REQUIRE "johnpye/iapws_sat_curves.a4c";


MODEL absorber;
	(* assumptions: 
		outlet is saturated steam
		inlet is saturated water at the specified pressure
		no pressure drop
		no temperature change
		all Q is absorbed by water
		steam generation is constant along length as mass rate, so x rises linearly.
	*)
	S_out IS_A iapws95_2phase; (* outlet steam state *)
	sat IS_A iapws_sat_density;
	T ALIASES S_out.T;
	T,sat.T ARE_THE_SAME;
	rho_gas ALIASES S_out.rho;
	rho_gas, sat.rhog ARE_THE_SAME;

	p ALIASES S_out.p;

	mdot_water_in IS_A mass_rate;
	mdot_water_out IS_A mass_rate;
	mdot_gas_out IS_A mass_rate;
	Vdot_gas_out IS_A volume_rate;
	mdot_out ALIASES mdot_water_in;

	m_water IS_A mass;
	m_gas IS_A mass;

	Q IS_A energy_rate; (* heat absorbed *)

	(* assume saturated water at inlet, so any heat added immediately creates some steam *)
	Hdot_in IS_A energy_rate;
	Hdot_out IS_A energy_rate;
	h_water IS_A specific_enthalpy;
	z01: h_water = 400 {kJ/kg} + p / (1000 {kg/m^3});

	z02: Hdot_in = mdot_water_in * h_water;
	z03: Hdot_out = mdot_water_out * h_water + mdot_gas_out * S_out.h;

	(* 1st law thermo *)
	z04: Q = Hdot_out - Hdot_in;

	(* mass conservation *)
	z05: mdot_water_in = mdot_water_out + mdot_gas_out;
 
	x_exit IS_A fraction;
	z06: x_exit * mdot_water_in = mdot_gas_out;

	(* assume that steam evolves linearly along length, so average x allow mass of water to be calculated *)
	x IS_A fraction;
	z07: x = (0 + x_exit)/2;
	
	(* assuming a slip-ratio of 1, we can get the average void ratio, eq 2.13 from Behnia *)
	alpha IS_A fraction;
	z08: alpha * S_out.rho * (1-x) = 1000{kg/m^3} * x * (1-alpha);

	z09: m_water = 1000{kg/m^3} * (1-alpha)*V_total;
	z10: m_gas = S_out.rho * alpha*V_total;

	z11: Vdot_gas_out = mdot_gas_out / rho_gas;
	V_total IS_A volume;
	
METHODS
METHOD default_self;
	RUN reset;
	RUN values;
END default_self;
METHOD specify;
	FIX V_total, mdot_water_in, Q, T;
END specify;
METHOD values;
	V_total := 300{m} * 16 * 1{PI}*( 40{mm} )^2;
	mdot_water_in := 0.4 {kg/s};
	Q := 800 {W/m^2} * 27(*concentration*) * 500{mm} * 60{m};
	T := 500 {K};
	(* free vars *)
END values;

END absorber;


(*
	This model seems completely correct but it won't converge.
	It's a problem with the S_out converging from defined (p,h).

	Need to investivate
*)
MODEL absorber2;
	S_in IS_A iapws95_2phase;
	S_out IS_A iapws95_2phase;
	mdot_in IS_A mass_rate;
	mdot_out IS_A mass_rate;
	Q IS_A energy_rate;
	m_water IS_A mass;
	V_total IS_A volume;

	H_in IS_A energy_rate;
	H_in = mdot_in*S_in.h;
	H_out IS_A energy_rate;
	H_out = mdot_out*S_out.h;
	
	Q = H_out - H_in;
	
	mdot_out = mdot_in;
	S_out.T = S_in.T; (* only valid so long as outlet is saturated as wel!!!!*)
	
	x_avg IS_A fraction;
	alpha IS_A fraction;
	x_avg = (S_in.x + S_out.x) / 2;
	alpha * S_out.rho * (1-x_avg) = 1000{kg/m^3} * x_avg * (1-alpha);

	m_water = S_in.rhol * (1-alpha) * V_total;

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

METHOD scale_self;
	S_out.Sl.rho.nominal := 800 {kg/m^3};
END scale_self;

METHOD specify;
	FIX V_total, Q;
	FIX mdot_in, S_in.T, S_in.rho;
END specify;

METHOD values;
	V_total := 300{m} * 16 * 1{PI}*( 40{mm} )^2;
	mdot_in := 0.4 {kg/s};
	Q := 800 {W/m^2} * 27(*concentration*) * 500{mm} * 60{m};
	S_in.T := 175 {K} + 273.15 {K};
	S_in.rho := 892 {kg/m^3};

	(* free *)
	S_out.T := S_in.T;
	S_out.rho := S_in.rho;
END values;

END absorber2;
1	REQUIRE "johnpye/iapws95.a4c";
2	REQUIRE "johnpye/iapws_sat_curves.a4c";
3
4
5	MODEL absorber;
6	(* assumptions:
7	outlet is saturated steam
8	inlet is saturated water at the specified pressure
9	no pressure drop
10	no temperature change
11	all Q is absorbed by water
12	steam generation is constant along length as mass rate, so x rises linearly.
13	*)
14	S_out IS_A iapws95_2phase; (* outlet steam state *)
15	sat IS_A iapws_sat_density;
16	T ALIASES S_out.T;
17	T,sat.T ARE_THE_SAME;
18	rho_gas ALIASES S_out.rho;
19	rho_gas, sat.rhog ARE_THE_SAME;
20
21	p ALIASES S_out.p;
22
23	mdot_water_in IS_A mass_rate;
24	mdot_water_out IS_A mass_rate;
25	mdot_gas_out IS_A mass_rate;
26	Vdot_gas_out IS_A volume_rate;
27	mdot_out ALIASES mdot_water_in;
28
29	m_water IS_A mass;
30	m_gas IS_A mass;
31
32	Q IS_A energy_rate; (* heat absorbed *)
33
34	(* assume saturated water at inlet, so any heat added immediately creates some steam *)
35	Hdot_in IS_A energy_rate;
36	Hdot_out IS_A energy_rate;
37	h_water IS_A specific_enthalpy;
38	z01: h_water = 400 {kJ/kg} + p / (1000 {kg/m^3});
39
40	z02: Hdot_in = mdot_water_in * h_water;
41	z03: Hdot_out = mdot_water_out * h_water + mdot_gas_out * S_out.h;
42
43	(* 1st law thermo *)
44	z04: Q = Hdot_out - Hdot_in;
45
46	(* mass conservation *)
47	z05: mdot_water_in = mdot_water_out + mdot_gas_out;
48
49	x_exit IS_A fraction;
50	z06: x_exit * mdot_water_in = mdot_gas_out;
51
52	(* assume that steam evolves linearly along length, so average x allow mass of water to be calculated *)
53	x IS_A fraction;
54	z07: x = (0 + x_exit)/2;
55
56	(* assuming a slip-ratio of 1, we can get the average void ratio, eq 2.13 from Behnia *)
57	alpha IS_A fraction;
58	z08: alpha * S_out.rho * (1-x) = 1000{kg/m^3} * x * (1-alpha);
59
60	z09: m_water = 1000{kg/m^3} * (1-alpha)*V_total;
61	z10: m_gas = S_out.rho * alpha*V_total;
62
63	z11: Vdot_gas_out = mdot_gas_out / rho_gas;
64	V_total IS_A volume;
65
66	METHODS
67	METHOD default_self;
68	RUN reset;
69	RUN values;
70	END default_self;
71	METHOD specify;
72	FIX V_total, mdot_water_in, Q, T;
73	END specify;
74	METHOD values;
75	V_total := 300{m} * 16 * 1{PI}*( 40{mm} )^2;
76	mdot_water_in := 0.4 {kg/s};
77	Q := 800 {W/m^2} * 27(concentration) * 500{mm} * 60{m};
78	T := 500 {K};
79	(* free vars *)
80	END values;
81
82	END absorber;
83
84
85	(*
86	This model seems completely correct but it won't converge.
87	It's a problem with the S_out converging from defined (p,h).
88
89	Need to investivate
90	*)
91	MODEL absorber2;
92	S_in IS_A iapws95_2phase;
93	S_out IS_A iapws95_2phase;
94	mdot_in IS_A mass_rate;
95	mdot_out IS_A mass_rate;
96	Q IS_A energy_rate;
97	m_water IS_A mass;
98	V_total IS_A volume;
99
100	H_in IS_A energy_rate;
101	H_in = mdot_in*S_in.h;
102	H_out IS_A energy_rate;
103	H_out = mdot_out*S_out.h;
104
105	Q = H_out - H_in;
106
107	mdot_out = mdot_in;
108	S_out.T = S_in.T; (* only valid so long as outlet is saturated as wel!!!!*)
109
110	x_avg IS_A fraction;
111	alpha IS_A fraction;
112	x_avg = (S_in.x + S_out.x) / 2;
113	alpha * S_out.rho * (1-x_avg) = 1000{kg/m^3} * x_avg * (1-alpha);
114
115	m_water = S_in.rhol * (1-alpha) * V_total;
116
117	METHODS
118	METHOD default_self;
119	RUN reset; RUN values;
120	RUN scale_self;
121	END default_self;
122
123	METHOD scale_self;
124	S_out.Sl.rho.nominal := 800 {kg/m^3};
125	END scale_self;
126
127	METHOD specify;
128	FIX V_total, Q;
129	FIX mdot_in, S_in.T, S_in.rho;
130	END specify;
131
132	METHOD values;
133	V_total := 300{m} * 16 * 1{PI}*( 40{mm} )^2;
134	mdot_in := 0.4 {kg/s};
135	Q := 800 {W/m^2} * 27(concentration) * 500{mm} * 60{m};
136	S_in.T := 175 {K} + 273.15 {K};
137	S_in.rho := 892 {kg/m^3};
138
139	(* free *)
140	S_out.T := S_in.T;
141	S_out.rho := S_in.rho;
142	END values;
143
144	END absorber2;