 # Diff of /trunk/models/johnpye/compressible_flow.a4c

revision 2457 by jpye, Fri Apr 15 03:10:24 2011 UTC revision 2458 by jpye, Mon Apr 18 08:15:12 2011 UTC
# Line 80  MODEL air_duct_node REFINES ideal_gas_du Line 80  MODEL air_duct_node REFINES ideal_gas_du
80      k :== 1.4;      k :== 1.4;
81  END air_duct_node;  END air_duct_node;
82
83    (*-----------------------NORMAL SHOCK IN ISENTROPIC FLOW----------------------*)
84
85  (*  (*
86      Model of a stationary normal shock in air. Using a moving frame of      Model of a stationary normal shock in air. Using a moving frame of
# Line 98  MODEL air_normal_shock; Line 99  MODEL air_normal_shock;
99      S2.T / S1.T = ( 1 + (k-1)/2*S1.M^2) * (2*k/(k-1)*S1.M^2 - 1)/ ((k+1)^2/2/(k-1)*S1.M^2);      S2.T / S1.T = ( 1 + (k-1)/2*S1.M^2) * (2*k/(k-1)*S1.M^2 - 1)/ ((k+1)^2/2/(k-1)*S1.M^2);
100  END air_normal_shock;  END air_normal_shock;
101
102    (*------------------------------EXAMPLE MODELS -------------------------------*)
103
104    (*
105        This model reproduces the results of Example 9.5 from Potter & Wiggert,
106        3rd SI edition. The question asks to determine the pressure and temperature
107        conditions downstream of a shock wave passing through ambient air of given
108        state.
109
110        Tested, works OK -- JP
111    *)
112    MODEL example_potter_wiggert_ex_9_5 REFINES air_normal_shock;
113    METHODS
115        FIX S1.Vel, S1.p, S1.T;
116        S1.Vel := 450 {m/s};
117        S1.p := 80 {kPa};
118        S1.T := 15 {K} + 273.15 {K};
120    END example_potter_wiggert_ex_9_5;
121
122    (*
123        This model reproduces the results of Example 9.5 from Potter & Wiggert,
124        3rd SI edition. This problem shows the wind speeds implicit behind a strong
125        shock wave such as that arising from a high-powered bomb explosions.
126
127        Although the problem as given in P&W can be solved even without doing so,
128        we have added an assumption that the ambient air pressure is 101.3 kPa. This
129        allows the model to be 'square' and the pressure and temperature behind the
130        shock wave (4.83 bar, 500 K) to also be calculated.
131
132        Tested, works OK -- JP
133    *)
134    MODEL example_potter_wiggert_ex_9_6 REFINES air_normal_shock;
135        Vel_induced IS_A speed;
136        Vel_induced = S2.Vel - S1.Vel;
137    METHODS
139        FIX S1.Vel, S1.T, S1.p;
140        S1.Vel := 700 {m/s};
141        S1.T := 15 {K} + 273.15 {K};
142        S1.p := 101.3 {kPa};
144    END example_potter_wiggert_ex_9_6;
145
146
147    (*----------------------------STAGNATION CONDITIONS---------------------------*)
148
149  (*  (*
150      Model of isentropic flow in a converging or diverging nozzle over an      Model of isentropic flow in a converging or diverging nozzle over an
151      interval in which no shock is present.      interval in which no shock is present.
243  END isentropic_stagnation_test_2;  END isentropic_stagnation_test_2;
244
245  (*------------------------------EXAMPLE MODELS -------------------------------*)
246
247
248    (*
249        Example 9.7 from Potter & Wiggert, 3rd SI edition. A converging-diverging
250        nozzle with normal shock at the exit plane, exiting to ambient conditions.
251        Exit diameter and throat diameter given. We calculate receiver pressure and
252        flow rate.
253
254        Note:
255        * throat must be at M = 1
256        * isentropic flow from throat to exit occurs with area ratio given
257        * upstream (reservoir) conditions are 90 kPa, 20 °C - ambient.
258    *)
259    MODEL example_potter_wiggert_ex_9_7 REFINES air_normal_shock;
260
261
262
263
264  (*  (*
265      Flow from reservoir at 20°C, 500 kPa to receiver at 300 kPa.      Flow from reservoir at 20°C, 500 kPa to receiver at 300 kPa.
290  END example_potter_wiggert_ex_9_2;  END example_potter_wiggert_ex_9_2;
291
(*
This model reproduces the results of Example 9.5 from Potter & Wiggert,
3rd SI edition. The question asks to determine the pressure and temperature
conditions downstream of a shock wave passing through ambient air of given
state.

Tested, works OK -- JP
*)
MODEL example_potter_wiggert_ex_9_5 REFINES air_normal_shock;
METHODS
FIX S1.Vel, S1.p, S1.T;
S1.Vel := 450 {m/s};
S1.p := 80 {kPa};
S1.T := 15 {K} + 273.15 {K};
END example_potter_wiggert_ex_9_5;

(*
This model reproduces the results of Example 9.5 from Potter & Wiggert,
3rd SI edition. This problem shows the wind speeds implicit behind a strong
shock wave such as that arising from a high-powered bomb explosions.

Although the problem as given in P&W can be solved even without doing so,
we have added an assumption that the ambient air pressure is 101.3 kPa. This
allows the model to be 'square' and the pressure and temperature behind the
shock wave (4.83 bar, 500 K) to also be calculated.

Tested, works OK -- JP
*)
MODEL example_potter_wiggert_ex_9_6 REFINES air_normal_shock;
Vel_induced IS_A speed;
Vel_induced = S2.Vel - S1.Vel;
METHODS
FIX S1.Vel, S1.T, S1.p;
S1.Vel := 700 {m/s};
S1.T := 15 {K} + 273.15 {K};
S1.p := 101.3 {kPa};
END example_potter_wiggert_ex_9_6;

292
(*
Example 9.5 from Potter & Wiggert, 3rd SI edition. A converging-diverging
nozzle with normal shock at the exit plane, exiting to ambient conditions.
Exit diameter and throat diameter given. We calculate supply pressure and
flow rate.
*)(*
MODEL example_potter_wiggert_ex_9_7 REFINES air_normal_shock;
*)
293

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