carbatpy.models.components.class_he

Created on Thu Jul 25 16:42:44 2024 heat-exchanger class

@author: welp

Attributes

now

Classes

HeatExchanger

Static heat exchanger model for counterflow configurations.

Module Contents

class carbatpy.models.components.class_he.HeatExchanger(fluids, inlet_states, mdot, resolution, ht_method, pl_method)

Static heat exchanger model for counterflow configurations.

Supports double-pipe and monoblock geometries. Heat exchanger profiles are computed by integrating coupled enthalpy and pressure ODEs along the tube length using scipy.integrate.solve_ivp.

Two inlet-state conventions are available:

• One-side IVP (calc_IVP_one_side()): Both inlet states are provided for the same side (inlet–outlet pair). Avoids the internal root-finding step and is the recommended approach.

• Two-side IVP (calc_IVP()): True counterflow setup — inlet states are given for both fluid inlets (left and right end). Requires an internal root-find to determine the unknown starting conditions.

Geometry Options

• Double-pipe (geo_double_pipe()): Annular secondary-fluid channel around an inner tube carrying the working fluid.

• Monoblock (geo_monoblock()): Two parallel tubes embedded in a solid conductive block. Thermal coupling is via the block material, using the VDI Heat Atlas shape factor for two eccentric cylinders.

param fluids:

Two-element list [working_fluid, secondary_fluid]. Each fluid must expose a set_state method compatible with carbatpy.fprop.

type fluids:

list of fluid objects

param inlet_states:

Two-element list [state_in_wf, state_in_sf]. Each state is the standard carbatpy property array (T, p, h, v, s, q, u, …).

type inlet_states:

list of array_like

param mdot:

Two-element list [mdot_wf, mdot_sf]. Mass flow rates in kg/s.

type mdot:

list of float

param resolution:

Number of spatial evaluation points along the heat exchanger length.

type resolution:

int

param ht_method:

Heat transfer correlation for the working fluid passed to heat_transfer.alpha_km. Example: "Deng_et_al-2019".

type ht_method:

str

param pl_method:

Pressure-loss correlation for the working fluid passed to heat_transfer.alpha_km. Example: "Macdonald_et_al-2016".

type pl_method:

str

state_array_wf

Fluid-property states along the heat exchanger for the working fluid.

Type:

ndarray, shape (n, n_props)

state_array_sf

Fluid-property states along the heat exchanger for the secondary fluid.

Type:

ndarray, shape (n, n_props)

x

Axial positions [m] corresponding to the state arrays.

Type:

ndarray

alpha_wf

Local heat transfer coefficients of the working fluid [W/(m²·K)].

Type:

list of float

alpha_sf

Local heat transfer coefficients of the secondary fluid [W/(m²·K)].

Type:

list of float

dpdl_wf

Local pressure-loss gradients of the working fluid [Pa/m].

Type:

list of float

dpdl_sf

Local pressure-loss gradients of the secondary fluid [Pa/m].

Type:

list of float

termination_flag

Name of the termination-event function that stopped the ODE solver, or None if the solver reached the end of the integration interval.

Type:

str or None

termination_position

Axial position [m] at which termination occurred, or None.

Type:

float or None

Examples

Double-pipe condenser solved with the one-side IVP method:

>>> import carbatpy as cb
>>> from class_he import HeatExchanger
>>> fluid1 = cb.init_fluid("Butane * CO2", [0.8, 0.2])
>>> fluid2 = cb.fprop.init_fluid("water", [1])
>>> st1_in = fluid1.set_state([3e6, 1], "PQ")
>>> st2_in = fluid2.set_state([st1_in[0] - 10, 3e5], "TP", cb.fprop._TRANS_STRING)
>>> he = HeatExchanger(
...     fluids=[fluid1, fluid2],
...     inlet_states=[st1_in, st2_in],
...     mdot=[0.01, 0.01],
...     resolution=40,
...     ht_method="Deng_et_al-2019",
...     pl_method="Macdonald_et_al-2016",
... )
>>> he.geo_double_pipe(16e-3, 18e-3, 22e-3, 40e-3, 40, 15.4)
>>> he.calc_IVP_one_side(case="wf_condensed")
>>> he.diagram()

See also

heat_transfer

Heat transfer and pressure-loss correlations used internally by thermal_resistance().

fluids

input_state_wf

input_state_sf

mdot_wf

mdot_sf

resolution

dT_wall = 5

ht_method

pl_method

geo_monoblock(d_wf, d_sf, r, l, lam_block)

Set monoblock heat exchanger geometry.

Two parallel circular tubes are embedded in a solid conductive block. The thermal coupling between them is computed via the VDI Heat Atlas (2013) shape factor for two cylinders in an infinite medium (Table E1-3).

Parameters:

• d_wf (float) – Inner diameter of the working-fluid tube [m].

• d_sf (float) – Inner diameter of the secondary-fluid tube [m].

• r (float) – Centre-to-centre distance between the two tubes [m].

• l (float) – Length of the block (and tubes) [m].

• lam_block (float) – Thermal conductivity of the block material [W/(m·K)].

Notes

The conduction shape factor for two cylinders in an infinite medium (VDI Heat Atlas 2013, E1 Table 3) is:

\[S = \frac{2\pi}{\mathrm{arccosh}\! \left(\frac{r^2 - r_{wf}^2 - r_{sf}^2} {2\, r_{wf}\, r_{sf}}\right)}\]

where \(r_{wf} = d_{wf}/2\) and \(r_{sf} = d_{sf}/2\).

geo_double_pipe(di, Di, da, Da, l, lam_tube)

Set double-pipe heat exchanger geometry.

The working fluid flows through the inner tube; the secondary fluid flows counter-currently through the annular gap between inner and outer tube.

Parameters:

• di (float) – Inner diameter of the inner tube (working-fluid side) [m].

• Di (float) – Outer diameter of the inner tube [m].

• da (float) – Inner diameter of the outer tube (secondary-fluid side) [m].

• Da (float) – Outer diameter of the outer tube [m].

• l (float) – Length of the pipe section [m].

• lam_tube (float) – Thermal conductivity of the inner-tube wall material [W/(m·K)].

Notes

The total heat transfer area referenced to the inner tube surface is set to \(A = \pi d_i l\).

The thermal resistance network (per unit length) is:

\[R_{tot} = \underbrace{\frac{1}{\alpha_{sf}\, \pi D_i}}_{R_{sf}} + \underbrace{\frac{\ln(D_i/d_i)}{2\pi\lambda_{tube}}}_{R_{tube}} + \underbrace{\frac{1}{\alpha_{wf}\, \pi d_i}}_{R_{wf}}\]

Examples

>>> he.geo_double_pipe(16e-3, 18e-3, 22e-3, 40e-3, 40, 15.4)

calc_IVP_one_side(verbose=False, wf_outlet=False, case=None, stop_value=0)

Calculate the heat exchanger by integrating the governing ODEs.

Both inlet states must be provided for the same physical side of the heat exchanger (i.e. an inlet–outlet pair, not two true inlets). The wf_outlet flag controls which end of the domain is used as the working-fluid inlet.

This is the recommended calculation method because it avoids the internal root-finding step required by calc_IVP().

Parameters:

• verbose (bool, default=False) – If True, print the solver status message.

• wf_outlet (bool, default=False) –

  Flow-direction flag.

  • False: working-fluid inlet is at \(x = 0\).

  • True: working-fluid inlet is at \(x = l\) (outlet side).

• case (str or None, default=None) –

  Optional early-termination criterion. Supported values:

  • 'sf_temperature_min' – stop when secondary-fluid temperature falls below stop_value [K].

  • 'sf_enthalpy_min' – stop when secondary-fluid enthalpy falls below stop_value [J/kg].

  • 'wf_enthalpy_min' – stop when working-fluid enthalpy falls below stop_value [J/kg].

  • 'wf_enthalpy_max' – stop when working-fluid enthalpy exceeds stop_value [J/kg].

  • 'wf_condensed' – stop when working fluid is fully condensed (vapour quality ≤ saturated-liquid enthalpy).

  • 'wf_evaporated' – stop when working fluid is fully evaporated (vapour quality ≥ saturated-vapour enthalpy).

• stop_value (float, default=0) – Threshold value used by the selected case. Unit depends on the chosen case (K or J/kg).

Returns:

Results are stored in state_array_wf, state_array_sf, x, alpha_wf, alpha_sf, dpdl_wf, dpdl_sf, termination_flag, and termination_position.

Return type:

None

Examples

>>> he.geo_double_pipe(16e-3, 18e-3, 22e-3, 40e-3, 40, 15.4)
>>> he.calc_IVP_one_side(verbose=True, case="wf_condensed")
>>> print(he.termination_flag)

calc_IVP(verbose=False, case=None, stop_value=0)

Calculate the heat exchanger using true counterflow inlet conditions.

Note

Not recommended. Use calc_IVP_one_side() instead, which avoids the internal root-finding step and is more robust.

Inlet states must be the true inlet states for both fluids — one at each end of the heat exchanger. An internal scipy.optimize.root call iterates on the unknown secondary-fluid state at \(x = 0\) until the prescribed secondary-fluid inlet condition at \(x = l\) is matched.

Parameters:

• verbose (bool, default=False) – If True, print the root-finder result and solver status.

• case (str or None, default=None) – Optional early-termination criterion (see calc_IVP_one_side() for supported values).

• stop_value (float, default=0) – Threshold for the selected case.

Returns:

Results are stored in state_array_wf, state_array_sf, x, alpha_wf, alpha_sf, dpdl_wf, and dpdl_sf.

Return type:

None

Raises:

ValueError – If the root-finder does not converge.

thermal_resistance(state_wf_x, state_sf_x)

Calculate the local total thermal resistance and pressure-loss gradients.

Dispatches to the correct resistance model based on self.geo_flag ("double_pipe" or "monoblock"), appends the local heat transfer coefficients and pressure-loss gradients to the instance lists, and updates self.dT_wall.

Parameters:

• state_wf_x (array_like) – Local carbatpy property array of the working fluid (T, p, h, …).

• state_sf_x (array_like) – Local carbatpy property array of the secondary fluid (T, p, h, …).

Returns:

• R_ges (float) – Total thermal resistance per unit length [(m·K)/W].

• dp_wf (float) – Pressure-loss gradient of the working fluid [Pa/m].

• dp_sf (float) – Pressure-loss gradient of the secondary fluid [Pa/m].

Notes

Double-pipe resistance network (per unit length):

\[R_{tot} = \frac{1}{\alpha_{sf}\,\pi D_i} + \frac{\ln(D_i/d_i)}{2\pi\lambda_{tube}} + \frac{1}{\alpha_{wf}\,\pi d_i}\]

Monoblock resistance network (per unit length):

\[R_{tot} = \frac{1}{\alpha_{sf}\,\pi d_{sf}} + \frac{1}{\lambda_{block}\, S} + \frac{1}{\alpha_{wf}\,\pi d_{wf}}\]

with the VDI shape factor \(S\) from geo_monoblock().

diagram(ordinate=0, second_yaxis=False, save_dir=None, show_plot=False)

Plot fluid-property profiles along the heat exchanger length.

The abscissa is the axial coordinate \(x\) [m]. The ordinate is selected by index, matching the column order of state_array_wf / state_array_sf:

• 0: Temperature [K]

• 1: Pressure [Pa]

• 2: Specific enthalpy [J/kg]

• 3: Specific volume [m³/kg]

• 4: Specific entropy [J/(kg·K)]

• 5: Vapour quality [–]

• 6: Specific internal energy [J/kg]

• 7: Dynamic viscosity [Pa·s]

• 8: Thermal conductivity [W/(m·K)]

• 9: Prandtl number [–]

• 10: Kinematic viscosity [m²/s]

• 11: Molar mass [kg/mol]

• 12: Speed of sound [m/s]

Parameters:

• ordinate (int, default=0) – Column index of the property to plot (see list above).

• second_yaxis (bool, default=False) – If True, working and secondary fluid are plotted on separate y-axes (useful when the two fluids have very different scales).

• save_dir (str or None, default=None) – Directory path for saving the figure as a PNG file. If None, the figure is only displayed.

• show_plot (bool, default=False) – If “True”, plots are shown.

Return type:

None

Examples

>>> he.calc_IVP_one_side()
>>> he.diagram()                        # temperature profile
>>> he.diagram(ordinate=1, second_yaxis=True)  # pressure, dual axes
>>> he.diagram(ordinate=2, save_dir=r"C:/results")  # save enthalpy plot

calculate_arrays(save_dir=None)

Export calculation results to CSV files and a termination-event log.

Writes three files to save_dir:

• wf.csv: Working-fluid state array with columns T, p, h, v, s, q, u, alpha_wf, dpdl_wf, tcx, vis. tcx and vis are the saturated-liquid thermal conductivity and viscosity where the vapour quality is ≥ 0; otherwise 0.

• sf.csv: Secondary-fluid state array with columns T, p, h, v, s, q, u, eta, tcx, Pr, cp, ws, M, alpha_sf, dpdl_sf.

• termination_event.txt: Plain-text log of termination_flag and termination_position.

Parameters:

save_dir (str) – Absolute path to an existing directory where the files will be saved.

Returns:

• df_wf (DataFrame)

• df_wf (DataFrame)

carbatpy.models.components.class_he.now