diff --git a/Tests/Data/Parabolic/T/BHE_1P/BHE_1P.prj b/Tests/Data/Parabolic/T/BHE_1P/BHE_1P.prj index c0a197093dda44a3692bd78cbd42d9e2d3ef17bc..636d81c8336bd674c0356fb44cea23b0b0f38357 100644 --- a/Tests/Data/Parabolic/T/BHE_1P/BHE_1P.prj +++ b/Tests/Data/Parabolic/T/BHE_1P/BHE_1P.prj @@ -141,27 +141,11 @@ <time_stepping> <type>FixedTimeStepping</type> <t_initial> 0.0 </t_initial> - <t_end> 600 </t_end> + <t_end> 432000 </t_end> <timesteps> <pair> - <repeat>60</repeat> - <delta_t>60</delta_t> - </pair> - <pair> - <repeat>60</repeat> - <delta_t>360</delta_t> - </pair> - <pair> - <repeat>41</repeat> - <delta_t>3600</delta_t> - </pair> - <pair> - <repeat>16</repeat> - <delta_t>43200</delta_t> - </pair> - <pair> - <repeat>28</repeat> - <delta_t>86400</delta_t> + <repeat>30</repeat> + <delta_t>14400</delta_t> </pair> </timesteps> </time_stepping> diff --git a/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md b/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md index bfd9bba7c02ef73e36716a505414578347be2611..2d8fba495c43117cb02a915add18ad2c7288e8ee 100644 --- a/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md +++ b/Tests/Data/Parabolic/T/BHE_1P/pipe_flow_ebhe.md @@ -10,10 +10,10 @@ project = ["Parabolic/T/BHE_1P/BHE_1P.prj"] ## Problem description -(Ramey et al. (1962)) proposed the analytical solution concerning the wellbore heat transmission, which can be used to quantify the fluid temperature change in the wellbore. -In order to verify the single pipe flow model in the OGS, the numerical results were compared with Ramey's analytical solution (Ramey et al. (1962)). +Ramey et al. (1962) proposed the analytical solution concerning the wellbore heat transmission, which can be used to quantify the fluid temperature change in the wellbore. +In order to verify the single pipe flow model in the OGS, the numerical results were compared with Ramey's analytical solution Ramey et al. (1962). The detailed calculation of the Ramey's analytical solution is given below. -A detailed analysis of an enhanced U-tube borehole heat exchanger (EUBHE) can be found in (Chen, C. et al. (2021)). +A detailed analysis of an enhanced U-tube borehole heat exchanger (EUBHE) can be found in Chen, C. et al. (2021). ## Model Setup @@ -57,10 +57,10 @@ lambda_pi = 1.3 r_pi = 0.12913 # Inner radius of pipe and wellbore r_b = 0.14 t_pi = 0.00587 # Thickness of the pipe -t = 86400 * 30 # Operation time +t = 86400 * 5 # Operation time ``` -In Ramey's analytical solution (Ramey et al. (1962)), the outlet temperature of the pipe inside the wellbore can be calculated by +In Ramey's analytical solution Ramey et al. (1962), the outlet temperature of the pipe inside the wellbore can be calculated by $$ T_o(t) = T_{s} + (T_i(t) - T_{s})\exp(-\Delta z/X) @@ -142,7 +142,7 @@ Re = rho_f * v * (2 * r_pi) / mu_f ``` -The Nusselt number can be determined by the following equation (Diersch, (2011)): +The Nusselt number can be determined by the following equation Diersch, (2011): $$ \mathrm{Nu} = 4.364,\ \mathrm{Re} < 2300 @@ -152,8 +152,6 @@ $$ \mathrm{Nu} = \frac{(\xi_{k}/8)\ \mathrm{Re}_{k}\ \mathrm{Pr}}{1+12.7\sqrt{{\xi_k}/8}(\mathrm{Pr}^{2/3}-1)} [ 1+(\frac{{d_k}^{i}}{L})^{2/3}], Re \geq 10^4 $$ -$$ - $$ \mathrm{Nu} = (1-\gamma_{k})\ 4.364 + \gamma_{k} ( \frac{(0.0308/8)10^{4}\mathrm{Pr}}{1+12.7\ \sqrt{0.0308/8}(\mathrm{Pr}^{2/3}-1)} \left[ 1+\left(\frac{d_{k}^{i}}{L}\right)^{2/3} \right] ), 2 300 \leq \mathrm{Re} < 10^{4} $$ @@ -206,7 +204,7 @@ h = lambda_f * Nu_p / (2 * r_pi) # Unit: W/m2/K U = 1 / (((r_pi + t_pi) / (r_pi * h)) + (r_pi + t_pi) * (np.log((r_pi + t_pi) / r_pi) / lambda_pi + np.log(r_b / (r_pi + t_pi)) / lambda_g)) ``` -The friction factor $f$, is evaluated by Churchill correlation (Churchill et al. (1977)), +The friction factor $f$, is evaluated by Churchill correlation Churchill et al. (1977), $$ f = \frac{1}{(\frac{1}{[((\frac{8}{Re})^{10}+(\frac{Re}{36500})^{20})]^{1/2}}+[2.21(\ln{\frac{Re}{7}})]^{10})^{1/5}} @@ -337,8 +335,8 @@ for delta_z in Z: # Plot numerical vs. analytical result fig, ax1 = plt.subplots(figsize=(10, 8)) -x_pos = np.arange(0, 2592000+60*60*24*5, 60*60*24*5) -x_ticks = np.arange(0,35,5) +x_pos = np.arange(0, 432000, 60*60*24) +x_ticks = np.arange(0,5,1) ax1.plot(time_range, df.iloc[-1, :], 'k.', markersize=10, markerfacecolor='none', label = 'Ramey\'s analytical solution')