Heat Exchanger (G-G)

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Heat exchanger for dual gas flow systems.

blockType: EngeeFluids.HeatExchangers.EffectivenessNTU.GasGas

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/Physical Modeling/Fluids/Heat Exchangers/Gas/Heat Exchanger (G-G)

Description

The block Heat Exchanger (G-G) simulates a gas-to-gas heat exchanger. The heat exchanger wall has thermal inertia capable of storing heat, which introduces a time delay in energy transfer proportional to its thermal mass. Both heat transfer fluids are homogeneous in phase state and are gases; phase transition in the process is excluded, which determines an exclusively contact heat exchange (no latent heat).

heat exchanger g g 1

Heat transfer model

The unit heat transfer model is based on the efficiency-number of heat transfer units (E-NTU) method. In steady-state, heat transfer occurs with an efficiency equal to only a fraction of the ideal value, which is achievable with no thermal resistance and constant inlet stream temperatures:

where

- is the actual heat flux;
- ideal heat flux;
- the fraction of the ideal heat flux actually observed in the actual heat exchanger that has losses. This quantity determines the efficiency of the heat exchanger and is a function of the number of transfer units, or .

The dimensionless parameter reflects the relative efficiency of interflow heat transfer compared to the ability of the flows to store the transferred heat:

where

- is the heat transfer coefficient between the streams;
- is the minimum value of the stream heat capacity related to the stream with the lowest heat absorption capacity.

The flow heat capacity depends on the specific heat capacity of the heat transfer fluid ( ) and on its mass flow rate through the heat exchanger ( ):

The efficiency also depends on the mutual arrangement of the flows, the number of strokes between them and the mixing conditions of the flows. Each flow pattern has its own efficiency expression. The list of such expressions is given in block Heat exchanger efficiency. The heat transfer fluid properties used by the block in heat transfer calculations are defined as the average between the volumetric and inlet values.

Heat transfer fluid flow diagram

The parameters Flow arrangement determines the mutual direction of the flows: straight flow, counter flow, across each other (cross flow), as well as the pipe-in-casing design, where one flow is inside the pipes and the other flow is outside, in the casing. The figure below illustrates such a flow pattern. The flow in the tubes can be either a single stroke through the casing (right) or multiple strokes (left) for greater heat transfer efficiency.

heat exchanger g g 2

Alternative fluid flow patterns can be specified from the general parameterization by tabulated efficiency data, which does not require detailed heat exchanger specification. Such data should reflect the flow pattern of the heat transfer fluids, the degree of mixing and the number of passages through the shell or tube.

Mixing conditions

The parameters Cross flow type allow the mixing character to be set: one of the flows is mixed, both or neither. Mixing implies a transverse movement of the heat transfer medium in ducts without internal barriers (guides, baffles, ribs or walls). It favours the equalisation of temperature gradients across the cross-section. In unmixed flows, as shown in the figure below on the right, the temperature varies only along the flow direction, while in mixed flows (figure on the left) it varies both longitudinally and transversely.

heat exchanger g g 3 en

The difference between mixed and unmixed flows is only taken into account in cross-flow schemes, where the longitudinal temperature change in one fluid induces transverse temperature gradients in the other. In direct/countercurrent flow schemes, only longitudinal temperature changes of the coolants occur and mixing practically does not affect heat transfer, therefore it is not taken into account.

Efficiency curves

The most efficient are shell-and-tube multi-pass heat exchangers (iv.b-e in the figure for 2, 3 and 4 passages). Among the single pass heat exchangers, counterflow heat exchangers are the most efficient (ii) and direct flow heat exchangers are the least efficient (i).

Cross-flow heat exchangers occupy an intermediate position in efficiency and their efficiency depends on the degree of mixing. The highest is achieved when there is no mixing in both streams (iii.a), the lowest when both streams are mixed (iii.b). Mixing only the stream with the lowest heat capacity (iii.c) reduces the efficiency to a greater extent than mixing the stream with the highest value of stream heat capacity (iii.d).

heat exchanger g g 4

Thermal resistance

The total thermal resistance, , is the sum of the local resistances in the direction of heat transfer. These include: convection at the wall surface and heat conduction through the wall and fouled layers in the presence of deposits. The formula below is used to calculate the total resistance in the direction from gas 1 to gas 2:

where

and are convective heat transfer coefficients for gas 1 and 2;
and - coefficient of deposits on the wall on the side of gas 1 and 2;
and - areas of heat transfer surfaces on the gas side 1 and 2;
- thermal resistance of the wall.

heat exchanger g g 5 en

Wall thermal resistance and fouling coefficients are constants set in the unit parameters. At the same time, heat transfer coefficients are complex functions depending on the properties of the heat transfer fluid, flow geometry and wall friction. They are calculated based on empirical correlations between Reynolds, Nusselt and Prandtl numbers. The choice of a particular correlation depends on the flow pattern of the coolants and mixing conditions, and is described in detail in block E-NTU Heat Transfer, on which the block model is based.

Wall heat capacity

The wall is not only a thermal resistance, it also has heat capacity and is capable of storing heat within its mass. Heat storage delays the transition between steady-state regimes, so that a thermal disturbance on one side does not immediately affect the other. The delay persists until the heat fluxes on both sides are balanced. This delay depends on the heat capacity of the wall:

where

- is the specific heat capacity of the wall;
- wall mass.

The product of the specific heat capacity and wall mass gives the energy required to raise the wall temperature by one degree. Use the block parameter Wall thermal mass, to set this product. The parameters are used when Wall thermal dynamics is checked.

In low pressure systems, heat capacity can often be neglected. Low pressure provides a thin wall with such a fast transient response that it is almost instantaneous on the heat transfer timescale. The same cannot be said for the high-pressure systems common in Haber ammonia production, where pressures can exceed 200 atmospheres. To withstand the high pressure, the walls are often made thicker, and since their heat capacity is greater, the transition process is slower.

Uncheck Wall thermal dynamics, to ignore the thermal inertia of the wall, and speed up the simulation speed, by reducing the calculations. Tick Wall thermal dynamics, to account for wall thermal inertia where it has a noticeable effect. If necessary, experiment with the settings to determine if the wall heat capacity needs to be accounted for. If the simulation results differ significantly, and if simulation speed is not a significant factor, check the box Wall thermal dynamics.

If the heat capacity of the wall is considered, only half of the wall is considered. One half is located on gas side 1 and the other half is located on gas side 2. The heat capacity is evenly distributed between these halves:

Energy is stored in the wall. In the simple case where half of the wall is in steady state, the heat gained from the coolant is equal to the heat lost by the other half of the wall. The heat flux is determined by the E-NTU method for a wall without heat capacity (see block E-NTU Heat Transfer). The flow rate is positive for heat flows from side 1 of the heat exchanger to side 2:

In the transient state, the wall is in the process of accumulating or losing heat, and the heat gained by one half is no longer equal to the heat lost by the other half. The difference in heat flow rate changes with time in proportion to the rate at which the wall stores or loses heat. For side 1 of the heat exchanger:

where is the rate of temperature change in half of the wall. The product of this rate by the heat capacity of half of the wall gives the rate of heat accumulation in it. This rate is positive when the temperature increases and negative when it decreases. The closer the velocity is to zero, the closer the wall is to steady state. For side 2 of the heat exchanger:

Block structure

The block is a composite component built from simpler blocks. The gas flow on side 1 of the heat exchanger is modelled using the block Heat Exchanger Interface (G). A similar block is used to model the gas flow on side 2. The heat exchange through the wall between the flows is modelled by usage of the block E-NTU Heat Transfer.

heat exchanger g g engee

Ports

Conserving

# A1 — gas inlet or outlet
gas

Details

Inlet or outlet port for gas 1 on its corresponding side of the heat exchanger.

Program usage name

gas_port_a1

# B1 — gas inlet or outlet
gas

Details

Inlet or outlet port for gas 1 on its corresponding side of the heat exchanger.

Program usage name

gas_port_b1

# A2 — gas inlet or outlet
gas

Details

Inlet or outlet port for gas 2 on its corresponding side of the heat exchanger.

Program usage name

gas_port_a2

# B2 — gas inlet or outlet
gas

Details

Inlet or outlet port for gas 2 on its corresponding side of the heat exchanger.

Program usage name

gas_port_b2

Parameters

Common

# Flow arrangement — flow diagram of the heat transfer medium in the heat exchanger
Parallel or counter flow | Shell and tube | Cross flow | Generic - effectiveness table

Details

Parameters defining the mutual arrangement of the flows in the heat exchanger: direct flow, countercurrent, across each other (transverse), as well as the "pipe in shell" design, in which one flow passes inside the pipes and the other flows outside, in the shell.

Alternative flow patterns can be specified in an arbitrary efficiency table, which does not require a detailed heat exchanger specification.

Values	`Parallel or counter flow` \| `Shell and tube` \| `Cross flow` \| `Generic - effectiveness table`
Default value	`Parallel or counter flow`
Program usage name	`flow_arrangement_type`
Evaluatable	No

# Number of shell passes — number of flow passages in the casing before outlet

Details

Number of flow passages through the shell in a shell and tube heat exchanger.

Dependencies

To use this parameter, set the parameters Flow arrangement to . Shell and tube.

Default value	`1`
Program usage name	`shell_count`
Evaluatable	Yes

# Cross flow type — type of mixing in each channel
Both fluids mixed | Both fluids unmixed | Gas 1 mixed & Gas 2 unmixed | Gas 1 unmixed & Gas 2 mixed

Details

The type of mixing of the heat transfer fluids in each duct. Mixing in this context is the lateral movement of the heat transfer fluid as it travels along the duct to the outlet. The flows remain separate from each other. Non-mixing flows are often found in channels with plates, baffles, or fins. This characteristic affects the efficiency of the heat exchanger: unmixed flows are most efficient and mixed flows are less efficient.

Dependencies

To use this parameter, set the parameter Flow arrangement to . Shell and tube.

Values	`Both fluids mixed` \| `Both fluids unmixed` \| `Gas 1 mixed & Gas 2 unmixed` \| `Gas 1 unmixed & Gas 2 mixed`
Default value	`Both fluids mixed`
Program usage name	`cross_flow_type`
Evaluatable	No

# Number of heat transfer units vector, NTU — the number of heat transfer units at each reference point in the heat exchanger efficiency look-up table

Details

The number of heat transfer units at each anchor point in the heat exchanger efficiency search table. The table is two-dimensional and the independent coordinates are the number of heat transfer units and the heat capacity factor. The block interpolates and extrapolates the reference points to determine the efficiency at any value of the number of transfer units. Interpolation is done using a linear function and extrapolation is done to the nearest value.

The specified numbers must be greater than zero and monotonically increasing from left to right. The dimensionality of this vector must correspond to the number of rows in the table Effectiveness table, E(NTU,CR). If the table has rows and columns, the vector for the number of carry units must be the length of elements.

Dependencies

To use this parameter, set the Flow arrangement parameters to Generic - effectiveness table.

Default value	`[0.5, 1.0, 2.0, 3.0, 4.0, 5.0]`
Program usage name	`NTU_vector`
Evaluatable	Yes

# Thermal capacity ratio vector, CR — heat capacity coefficient at each reference point of the heat exchanger efficiency table

Details

The heat capacity coefficient values corresponding to the reference points in the heat exchanger efficiency table. The table is two-dimensional and the independent coordinates are the number of heat transfer units and the heat capacity factor. The block interpolates and extrapolates the reference points to determine the efficiency at any value of the heat capacity coefficient. Interpolation is done using a linear function, and extrapolation is done to the nearest value.

The coefficients must be positive and strictly increasing from left to right. The dimensionality of the vector should correspond to the number of columns in the table Effectiveness table, E(NTU,CR). If the table has rows and columns, the vector of heat capacity coefficients should be the length of elements.

The heat capacity coefficient is the ratio of the minimum and maximum values of the flux heat capacity.

Dependencies

To use this parameter, set the parameter Flow arrangement to . Generic - effectiveness table.

Default value	`[0.0, 0.25, 0.5, 0.75, 1.0]`
Program usage name	`C_ratio_vector`
Evaluatable	Yes

# Effectiveness table, E(NTU,CR) — heat exchanger efficiency at each reference point of the search table by number of transfer units and heat capacity coefficient

Details

Values of heat exchanger efficiency in reference points of a two-dimensional table specified by coordinates: number of heat transfer units and heat capacity coefficient. The block interpolates and extrapolates the table values to determine the efficiency at arbitrary combinations of these parameters. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The efficiency values must be non-negative. They should be ordered by rows in the order of increasing number of transfer units (from top to bottom), and by columns - in the order of increasing heat capacity coefficient (from left to right). The number of rows should correspond to the dimensionality of the vector Number of heat transfer units vector, NTU, and the number of columns to the dimensionality of the vector Thermal capacity ratio vector, CR.

Dependencies

To use this parameter, set the Flow arrangement parameter to the value of Generic - effectiveness table.

Default value	`[0.3 0.3 0.3 0.3 0.3; 0.6 0.55 0.5 0.47 0.43; 0.85 0.76 0.68 0.61 0.55; 0.94 0.83 0.72 0.65 0.58; 0.98 0.86 0.75 0.66 0.58; 0.99 0.86 0.75 0.66 0.58]`
Program usage name	`effectiveness_matrix`
Evaluatable	Yes

# Wall thermal dynamics — whether to take into account the thermal inertia of the wall

Details

Determines whether the thermal mass of the heat exchanger wall should be taken into account. Enabling this option results in a lag in the wall response to changes in temperature or heat flux. If the option Wall thermal dynamics is disabled, it is assumed that the wall is thin enough that its thermal response is instantaneous compared to the characteristic heat transfer time.

Default value	`false (switched off)`
Program usage name	`dynamic`
Evaluatable	No

# Wall thermal mass — heat required to raise the wall temperature by one degree
J/K | kJ/K

Details

The heat required to raise the wall temperature by one degree. Heat capacity is the product of mass by specific heat capacity and a measure of the ability to absorb heat. A wall with heat capacity has a transient response to sudden changes in surface temperature or heat flux. The greater the heat capacity, the slower this reaction and the longer the time to reach steady state. The value by default corresponds to a stainless steel wall with a mass of about 1 kg.

Dependencies

To use this parameter, tick the checkbox Wall thermal dynamics.

Units	`J/K` \| `kJ/K`
Default value	`447.0 J/K`
Program usage name	`wall_thermal_mass`
Evaluatable	Yes

# Wall thermal resistance — resistance of the wall to heat flow due to heat conduction
K/W

Details

The resistance of a wall to heat flow due to heat conduction and the inverse of thermal conductivity, or the product of thermal conductivity by the ratio of surface area to length. The wall resistance is added together with the convective and fouling resistance to determine the total heat transfer coefficient between the flows.

Units	`K/W`
Default value	`0.00016 K/W`
Program usage name	`R_wall`
Evaluatable	Yes

Gas 1

# Minimum free-flow area — cross-sectional area of the heat-carrier channel at the narrowest point
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Minimum cross-sectional area of of the channel through which the heat transfer fluid flows between the inlet and outlet. If it is a set of channels, tubes, slots or grooves, the parameter value is defined as the sum of the smallest areas at the point of minimum flow area. This parameter reflects the cross-section where the fluid velocity is maximum. For example, if the fluid flows perpendicular to a row of tubes, the value of this parameter is the sum of the gaps between the tubes in the cross section with the smallest gap area.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`min_flow_area_1`
Evaluatable	Yes

# Hydraulic diameter for pressure loss — hydraulic diameter of the channel at its narrowest point
m | cm | ft | in | km | mi | mm | um | yd

Details

The effective internal diameter of the channel at the cross-section with the smallest area. For non-circular channels, the hydraulic diameter is the equivalent diameter of a circle with an area equal to the area of the existing channel.

If the channel is given by a set of channels, pipes, slots or grooves, the total perimeter is equal to the sum of the perimeters of all elements. If the canal is a circular pipe, its hydraulic diameter is equal to its actual diameter.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`hydraulic_diameter_for_pressure_loss_1`
Evaluatable	Yes

# Gas volume — total volume of heat transfer fluid in gas channel 1
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

Total volume of heat transfer fluid contained in gas channel 1.

Units	`l` \| `gal` \| `igal` \| `m^3` \| `cm^3` \| `ft^3` \| `in^3` \| `km^3` \| `mi^3` \| `mm^3` \| `um^3` \| `yd^3` \| `Nm/Pa` \| `Nm/bar` \| `lbfft/psi` \| `ftlbf/psi`
Default value	`0.01 m^3`
Program usage name	`V_gas_1`
Evaluatable	Yes

# Laminar flow upper Reynolds number limit — lower boundary of the transition zone between laminar and turbulent flow regimes

Details

Reynolds number value corresponding to the lower boundary of the transition zone between laminar and turbulent flow regimes. Above this value, inertial forces begin to dominate, resulting in a transition from laminar to turbulent flow. The value by default corresponds to a round pipe with a smooth inner surface.

Default value	`2000.0`
Program usage name	`Re_laminar_1`
Evaluatable	Yes

# Turbulent flow lower Reynolds number limit — upper boundary of the transition zone between laminar and turbulent flow regimes

Details

The Reynolds number value corresponding to the upper boundary of the transition zone between laminar and turbulent flow regimes. Below this value, viscous forces begin to dominate, resulting in a transition from turbulent to laminar flow. The By default value corresponds to a round pipe with a smooth inner surface.

Default value	`4000.0`
Program usage name	`Re_turbulent_1`
Evaluatable	Yes

# Pressure loss model — mathematical model for calculating pressure losses due to viscous friction
Pressure loss coefficient | Correlation for flow inside tubes | Tabulated data - Darcy friction factor vs. Reynolds number | Tabulated data - Euler number vs. Reynolds number

Details

Parameters allows you to select one of the models for calculating pressure losses due to viscous friction. The parameter defines which expressions will be used in the calculation of the losses and which block parameters must be set as input. Details of the calculations depending on the selected parameterization are given in Friction.

Values	`Pressure loss coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Darcy friction factor vs. Reynolds number` \| `Tabulated data - Euler number vs. Reynolds number`
Default value	`Pressure loss coefficient`
Program usage name	`pressure_loss_type_1`
Evaluatable	No

# Pressure loss coefficient — total coefficient that takes into account hydraulic losses between ports

Details

The total loss coefficient that takes into account all hydraulic resistance to flow in the channel, including wall friction losses (major losses) and localised resistance due to bends, elbows and other geometry changes (minor losses).

The loss coefficient is an empirical dimensionless quantity widely used to describe pressure losses due to viscous friction. It can be calculated from experimental data or, in some cases, obtained from technical documentation.

Dependencies

To use this parameter, set the parameter Pressure loss model to . Pressure loss coefficient.

Default value	`0.1`
Program usage name	`pressure_loss_coefficient_1`
Evaluatable	Yes

# Length of flow path from inlet to outlet — distance travelled from port to port
m | cm | ft | in | km | mi | mm | um | yd

Details

The total distance the flow must travel between ports. In multi-pass shell-and-tube heat exchangers, the total distance is the sum of all the passes through the shell. In tube bundles, corrugated plates and other ducts where the flow is divided into parallel branches, it is the distance travelled per branch. The longer the flow path, the greater the basic pressure loss due to viscous friction against the walls.

Dependencies

To use this parameter, set the parameters Pressure loss model to the value of Correlation for flow inside tubes or Tabulated data - Darcy friction factor vs. Reynolds number.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`flow_path_length_1`
Evaluatable	Yes

# Aggregate equivalent length of local resistances — total local pressure loss, expressed in length
m | cm | ft | in | km | mi | mm | um | yd

Details

Total local pressure losses expressed in length. The length of the straight duct results in equivalent losses equal to the sum of the existing local resistances of branches, tees and connections. The greater the equivalent length, the higher the pressure losses due to local resistances.

Dependencies

To use this parameter, set the parameter Pressure loss model to . Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`flow_path_length_add_1`
Evaluatable	Yes

# Internal surface absolute roughness — average height of roughnesses on the wall surface that result in viscous friction losses
m | cm | ft | in | km | mi | mm | um | yd

Details

The average height of the roughnesses on the wall surface that result in viscous friction losses. The greater the average height, the rougher the wall and the greater the pressure loss due to viscous friction. The surface roughness value is used to derive the Darcy coefficient of friction from the Haaland relationship.

Dependencies

To use this parameter, set the parameter Pressure loss model to the value of Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`15e-6 m`
Program usage name	`roughness_1`
Evaluatable	Yes

# Reynolds number vector for Darcy friction factor — Reynolds number at each reference point in the Darcy friction coefficient look-up table

Details

Reynolds number at each reference point of the Darcy friction coefficient search table. The block interpolates and extrapolates the table values to determine the Darcy friction coefficient at any Reynolds number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the dimensionality of the vector Darcy friction factor vector for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[400.0, 1000.0, 1500.0, 3e3, 4e3, 6e3, 1e4, 2e4, 4e4, 6e4, 1e5, 1e8]`
Program usage name	`Re_friction_vector_1`
Evaluatable	Yes

# Darcy friction factor vector — Darcy friction coefficient at each reference point of the Reynolds number look-up table

Details

Darcy friction coefficient at each reference point in the Reynolds number lookup table. The block interpolates and extrapolates the table values to determine the Darcy friction coefficient at any Reynolds number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of the Darcy friction coefficient shall not be negative and shall line up from left to right in ascending order of the corresponding Reynolds numbers. The dimensionality of this vector should correspond to the dimensionality of the vector Reynolds number vector for Darcy friction factor for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Pressure loss model parameter to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[0.264, 0.112, 0.071, 0.0417, 0.0387, 0.0268, 0.0250, 0.0232, 0.0226, 0.0220, 0.0214, 0.0214]`
Program usage name	`friction_factor_vector_1`
Evaluatable	Yes

# Reynolds number vector for Euler number — Reynolds number at each reference point in the Euler number look-up table

Details

Reynolds number at each reference point of the Euler number search table. The block performs inter- and extrapolation of the table values to determine the Euler number at any Reynolds number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of the Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the dimensionality of the vector Euler number vector for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[50.0, 500.0, 1000.0, 2000.0]`
Program usage name	`Re_vector_Eu_1`
Evaluatable	Yes

# Euler number vector — Euler number at each reference point in the Reynolds number look-up table

Details

Euler number at each reference point of the Reynolds number search table. The block interpolates and extrapolates the table values to determine the Reynolds number at any Euler number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of the Darcy friction coefficient shall not be negative and shall line up from left to right in ascending order of the corresponding Reynolds numbers. The dimensionality of this vector should correspond to the dimensionality of the vector Reynolds number vector for Euler number for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[4.4505, 0.6864, 0.4791, 0.3755]`
Program usage name	`Eu_vector_1`
Evaluatable	Yes

# Heat transfer coefficient model — mathematical model for heat transfer between the coolant and the wall
Constant heat transfer coefficient | Correlation for flow inside tubes | Tabulated data - Colburn factor vs. Reynolds number | Tabulated data - Nusselt number vs. Reynolds number and Prandtl number

Details

Mathematical model for heat transfer between the heat transfer medium and the wall. The choice of model determines which expressions to apply and which parameters to specify for heat transfer calculations.

For more details see. Nusselt number.

Values	`Constant heat transfer coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Colburn factor vs. Reynolds number` \| `Tabulated data - Nusselt number vs. Reynolds number and Prandtl number`
Default value	`Constant heat transfer coefficient`
Program usage name	`heat_transfer_type_1`
Evaluatable	No

# Heat transfer surface area — effective surface area used in the heat transfer between the heat transfer medium and the wall
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Effective surface area used in heat transfer between a fluid and a wall. The effective surface area is the sum of the primary and secondary surface areas, the area where the wall is exposed to the fluid, and the fin area, if any, used. The fin surface area is usually calculated from the fin efficiency factor.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.4 m^2`
Program usage name	`heat_transfer_area_1`
Evaluatable	Yes

# Gas-wall heat transfer coefficient — heat transfer coefficient by convection between the coolant and the wall
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

Heat transfer coefficient for convection between the heat transfer medium and the wall. The resistance caused by fouling is considered separately in the parameters Fouling factor.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to . Constant heat transfer coefficient.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`100.0 W/(m^2*K)`
Program usage name	`alpha_const_1`
Evaluatable	Yes

# Length of flow path for heat transfer — pipe or duct length
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the pipe or duct from inlet to outlet.

Dependencies

To use this parameter, set the parameters Heat transfer coefficient model to Tabulated data - Colburn factor vs. Reynolds number or Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`length_for_heat_transfer_1`
Evaluatable	Yes

# Nusselt number for laminar flow heat transfer — constant value of Nusselt number for laminar flow

Details

Constant value of Nusselt number for laminar flows. The Nusselt number is required to calculate the heat transfer coefficient between the heat transfer medium and the wall. The value by default corresponds to a cylindrical pipe.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to the value of Correlation for flow inside tubes.

Default value	`3.66`
Program usage name	`Nu_laminar_1`
Evaluatable	Yes

# Reynolds number vector for Colburn factor — Reynolds number at each reference point of the Colburn factor look-up table

Details

Reynolds number at each reference point of the Colburn factor lookup table. The block performs inter- and extrapolation of the table values to determine the Colburn factor at any Reynolds number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the dimensionality of the vector Colburn factor vector for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_colburn_1`
Evaluatable	Yes

# Colburn factor vector — Colburn factor at each reference point in the Reynolds number look-up table

Details

Colburn factor at each reference point of the Reynolds number lookup table. The block interpolates and extrapolates the table values to determine the Reynolds number at any Colburn factor. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The Colburn factor values must not be negative and must line up from left to right in ascending order of the corresponding Reynolds numbers. The dimensionality of this vector should correspond to the dimensionality of the vector Reynolds number vector for Nusselt number for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameter to Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[0.019, 0.013, 0.002]`
Program usage name	`colburn_factor_vector_1`
Evaluatable	Yes

# Reynolds number vector for Nusselt number — Reynolds number at each reference point in the Nusselt number look-up table

Details

Reynolds number at each anchor point of the Nusselt number lookup table. The table is two-parameter, where Reynolds and Prandtl numbers are used as independent coordinates. The block performs inter- and extrapolation of the table values to determine the Nusselt number at any Reynolds number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the number of rows in the table Nusselt number table, Nu(Re,Pr). If the table has rows and columns, the Reynolds number vector must be of length elements.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_Nu_1`
Evaluatable	Yes

# Prandtl number vector for Nusselt number — Prandtl number at each reference point of the Nusselt number look-up table

Details

Prandtl number at each anchor point of the Nusselt number lookup table. The table is two-parameter, where Reynolds and Prandtl numbers are used as independent coordinates. The block performs inter- and extrapolation of the table values to determine the Nusselt number at any Prandtl number. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value.

The values of Prandtl numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the number of columns in the table Nusselt number table, Nu(Re,Pr). If the table has rows and columns, the Prandtl number vector must be of length elements.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[1.0, 10.0]`
Program usage name	`Pr_vector_Nu_1`
Evaluatable	Yes

# Nusselt number table, Nu(Re,Pr) — Nusselt number at each reference point of the Reynolds-Prandtl number search table

Details

Nusselt number at each reference point of the Reynolds-Prandtl number search table. The block interpolates and extrapolates the table values to determine the Nusselt number at any pair of Reynolds-Prandtl numbers. Interpolation is performed using a linear function, and extrapolation is performed to the nearest value. By determining the Nusselt number, the table provides the data for the calculation from which the heat transfer coefficient between the fluid and the wall is determined.

The Nusselt number must be greater than zero. Each value should be arranged from top to bottom in order of increasing Reynolds numbers and from left to right in order of increasing Prandtl numbers. The number of rows should be equal to the dimensionality of the vector Reynolds number vector for Nusselt number, and the number of columns should be equal to the dimensionality of the vector Prandtl number vector for Nusselt number.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to the value of Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[3.72 4.21; 3.75 4.44; 4.21 7.15]`
Program usage name	`Nu_matrix_1`
Evaluatable	Yes

# Fouling factor — thermal resistance due to deposits
K*m^2/W | deltadegR*ft^2*hr/Btu_IT

Details

Thermal resistance due to deposits that form over time on exposed wall surfaces. Deposits, because they create a new solid layer between the heat transfer medium and the wall through which heat must pass, add additional thermal resistance to the heat transfer path. The deposits grow slowly and the resistance caused by them is accordingly assumed to be constant during the simulation.

Units	`Km^2/W` \| `deltadegRft^2*hr/Btu_IT`
Default value	`1e-4 K*m^2/W`
Program usage name	`fouling_factor1`
Evaluatable	Yes

# Threshold mass flow rate for flow reversal — threshold mass flow rate
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The mass flow rate below which numerical smoothing is applied. This is to avoid discontinuities when the flow is stagnant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1e-4 kg/s`
Program usage name	`mdot_threshold_1`
Evaluatable	Yes

# Minimum fluid-wall heat transfer coefficient — lower limit for the heat transfer coefficient of the heat transfer medium
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

Lower limit for the heat transfer coefficient between the fluid and the wall. If the calculation gives a lower heat transfer coefficient, the value Minimum fluid-wall heat transfer coefficient replaces the calculated value.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`5.0 W/(m^2*K)`
Program usage name	`alpha1_min`
Evaluatable	Yes

Gas 2

# Minimum free-flow area — cross-sectional area of the heat-carrier channel at the narrowest point
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`min_flow_area_2`
Evaluatable	Yes

# Hydraulic diameter for pressure loss — hydraulic diameter of the channel at its narrowest point
m | cm | ft | in | km | mi | mm | um | yd

Details

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`hydraulic_diameter_for_pressure_loss_2`
Evaluatable	Yes

# Gas volume — total volume of coolant in the gas channel 2
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

Total volume of heat transfer fluid contained in gas channel 2.

Units	`l` \| `gal` \| `igal` \| `m^3` \| `cm^3` \| `ft^3` \| `in^3` \| `km^3` \| `mi^3` \| `mm^3` \| `um^3` \| `yd^3` \| `Nm/Pa` \| `Nm/bar` \| `lbfft/psi` \| `ftlbf/psi`
Default value	`0.01 m^3`
Program usage name	`V_gas_2`
Evaluatable	Yes

# Laminar flow upper Reynolds number limit — lower boundary of the transition zone between laminar and turbulent flow regimes

Details

Default value	`2000.0`
Program usage name	`Re_laminar_2`
Evaluatable	Yes

# Turbulent flow lower Reynolds number limit — upper boundary of the transition zone between laminar and turbulent flow regimes

Details

Default value	`4000.0`
Program usage name	`Re_turbulent_2`
Evaluatable	Yes

Details

Values	`Pressure loss coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Darcy friction factor vs. Reynolds number` \| `Tabulated data - Euler number vs. Reynolds number`
Default value	`Pressure loss coefficient`
Program usage name	`pressure_loss_type_2`
Evaluatable	No

# Pressure loss coefficient — total coefficient that takes into account hydraulic losses between ports

Details

Dependencies

To use this parameter, set the Pressure loss model parameters to Pressure loss coefficient.

Default value	`0.1`
Program usage name	`pressure_loss_coefficient_2`
Evaluatable	Yes

# Length of flow path from inlet to outlet — distance travelled from port to port
m | cm | ft | in | km | mi | mm | um | yd

Details

The total distance the flow must travel between ports. In multi-pass shell-and-tube heat exchangers, the total distance is the sum of all passes through the shell. In tube bundles, corrugated plates and other ducts where the flow is divided into parallel branches, it is the distance travelled per branch. The longer the flow path, the greater the basic pressure loss due to viscous friction against the walls.

Dependencies

To use this parameter, set the parameters Pressure loss model to the value of Correlation for flow inside tubes or Tabulated data - Darcy friction factor vs. Reynolds number.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`flow_path_length_2`
Evaluatable	Yes

# Aggregate equivalent length of local resistances — total local pressure loss, expressed in length
m | cm | ft | in | km | mi | mm | um | yd

Details

Dependencies

To use this parameter, set the parameter Pressure loss model to . Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`flow_path_length_add_2`
Evaluatable	Yes

# Internal surface absolute roughness — average height of roughnesses on the wall surface that result in viscous friction losses
m | cm | ft | in | km | mi | mm | um | yd

Details

Dependencies

To use this parameter, set the parameter Pressure loss model to the value of Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`15e-6 m`
Program usage name	`roughness_2`
Evaluatable	Yes

# Reynolds number vector for Darcy friction factor — Reynolds number at each reference point in the Darcy friction coefficient look-up table

Details

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[400.0, 1000.0, 1500.0, 3e3, 4e3, 6e3, 1e4, 2e4, 4e4, 6e4, 1e5, 1e8]`
Program usage name	`Re_friction_vector_2`
Evaluatable	Yes

# Darcy friction factor vector — Darcy friction coefficient at each reference point of the Reynolds number look-up table

Details

Dependencies

To use this parameter, set the Pressure loss model parameter to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[0.264, 0.112, 0.071, 0.0417, 0.0387, 0.0268, 0.0250, 0.0232, 0.0226, 0.0220, 0.0214, 0.0214]`
Program usage name	`friction_factor_vector_2`
Evaluatable	Yes

# Reynolds number vector for Euler number — Reynolds number at each reference point in the Euler number look-up table

Details

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[50.0, 500.0, 1000.0, 2000.0]`
Program usage name	`Re_vector_Eu_2`
Evaluatable	Yes

# Euler number vector — Euler number at each reference point in the Reynolds number look-up table

Details

The values of the Darcy friction coefficient shall not be negative and shall line up from left to right in ascending order of the corresponding Reynolds numbers. The dimensionality of this vector should correspond to the dimensionality of the vector Reynolds number vector for Euler number for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[4.4505, 0.6864, 0.4791, 0.3755]`
Program usage name	`Eu_vector_2`
Evaluatable	Yes

Details

For more details see. Nusselt number.

Values	`Constant heat transfer coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Colburn factor vs. Reynolds number` \| `Tabulated data - Nusselt number vs. Reynolds number and Prandtl number`
Default value	`Constant heat transfer coefficient`
Program usage name	`heat_transfer_type_2`
Evaluatable	No

Details

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.4 m^2`
Program usage name	`heat_transfer_area_2`
Evaluatable	Yes

# Gas-wall heat transfer coefficient — heat transfer coefficient by convection between the coolant and the wall
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

Heat transfer coefficient for convection between the heat transfer medium and the wall. The resistance caused by fouling is considered separately in the parameters Fouling factor.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to . Constant heat transfer coefficient.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`100.0 W/(m^2*K)`
Program usage name	`alpha_const_2`
Evaluatable	Yes

# Length of flow path for heat transfer — pipe or duct length
m | cm | ft | in | km | mi | mm | um | yd

Details

The length of the pipe or duct from inlet to outlet.

Dependencies

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`length_for_heat_transfer_2`
Evaluatable	Yes

# Nusselt number for laminar flow heat transfer — constant value of Nusselt number for laminar flow

Details

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to the value of Correlation for flow inside tubes.

Default value	`3.66`
Program usage name	`Nu_laminar_2`
Evaluatable	Yes

# Reynolds number vector for Colburn factor — Reynolds number at each reference point of the Colburn factor look-up table

Details

The values of Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the dimensionality of the vector Colburn factor vector for the calculation of tabulated reference points.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_colburn_2`
Evaluatable	Yes

# Colburn factor vector — Colburn factor at each reference point in the Reynolds number look-up table

Details

Dependencies

To use this parameter, set the Heat transfer coefficient model parameter to Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[0.019, 0.013, 0.002]`
Program usage name	`colburn_factor_vector_2`
Evaluatable	Yes

# Reynolds number vector for Nusselt number — Reynolds number at each reference point in the Nusselt number look-up table

Details

The values of Reynolds numbers must be greater than zero and monotonically increasing from left to right. They can cover laminar, transient and turbulent regimes. The dimensionality of this vector should correspond to the number of rows in the table Nusselt number table, Nu(Re,Pr). If the table has rows and columns, the Reynolds number vector must be of length elements.

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_Nu_2`
Evaluatable	Yes

# Prandtl number vector for Nusselt number — Prandtl number at each reference point of the Nusselt number look-up table

Details

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[1.0, 10.0]`
Program usage name	`Pr_vector_Nu_2`
Evaluatable	Yes

# Nusselt number table, Nu(Re,Pr) — Nusselt number at each reference point of the Reynolds-Prandtl number search table

Details

Dependencies

To use this parameter, set the parameter Heat transfer coefficient model to the value of Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[3.72 4.21; 3.75 4.44; 4.21 7.15]`
Program usage name	`Nu_matrix_2`
Evaluatable	Yes

# Fouling factor — thermal resistance due to deposits
K*m^2/W | deltadegR*ft^2*hr/Btu_IT

Details

Units	`Km^2/W` \| `deltadegRft^2*hr/Btu_IT`
Default value	`1e-4 K*m^2/W`
Program usage name	`fouling_factor2`
Evaluatable	Yes

# Threshold mass flow rate for flow reversal — threshold mass flow rate
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The mass flow rate below which numerical smoothing is applied. This is to avoid discontinuities when the flow is stagnant.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1e-4 kg/s`
Program usage name	`mdot_threshold_2`
Evaluatable	Yes

# Minimum fluid-wall heat transfer coefficient — lower limit for the heat transfer coefficient of the heat transfer medium
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`5.0 W/(m^2*K)`
Program usage name	`alpha2_min`
Evaluatable	Yes

Effects and Initial Conditions

Details

Temperature of gas 1 in the channel at the beginning of the simulation.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_start_1`
Evaluatable	Yes

# Gas 1 initial pressure — pressure of gas 1 in the channel at the beginning of the simulation
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Pressure of gas 1 in the channel at the beginning of the simulation.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_start_1`
Evaluatable	Yes

Details

Temperature of gas 2 in the channel at the beginning of the simulation.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_start_2`
Evaluatable	Yes

# Gas 2 initial pressure — pressure of gas 2 in the channel at the beginning of the simulation
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Gas pressure 2 in the channel at the beginning of the simulation.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_start_2`
Evaluatable	Yes