Local Resistance (TL)

Pipe resistance in a thermal liquid network

Since R2022a

Libraries:
Simscape / Fluids / Thermal Liquid / Pipes & Fittings

Description

The Local Resistance (TL) block represents pressure loss due to user-defined pipe resistance in a thermal liquid network. You can specify different loss coefficients for forward and reversed flows through the pipe segment. For pipe bends, you can also choose to use the Thermal Liquid library blocks Pipe Bend (TL) and Elbow (TL) or, for area changes, the Sudden Area Change (TL) block.

The loss factor is parameterized by either a constant relationship based on the pipe pressure or by user-supplied tabular data for loss coefficients based on the Reynolds number.

Constant Loss Factor

Segments with loss factors that remain constant over a range of flow velocities are calculated as:

$k_{l o s s} = k_{l o s s, B A} + \frac{(k_{l o s s, A B} - k_{l o s s, B A})}{2} [\tanh (\frac{3 Δ p}{Δ p_{c r i t}}) + 1],$

where:

k_loss,AB and k_loss,BA are the Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) parameters, respectively.
Δp is the pressure difference p_A – p_B.

The critical pressure difference, Δp_crit, is the pressure differential associated with the Critical Reynolds number, Re_crit, which is the flow regime transition point between laminar and turbulent flow:

$Δ p_{c r i t} = \frac{\bar{ρ}}{2} k_{l o s s, c r i t} {(\frac{ν {Re}_{c r i t}}{D_{h}})}^{2},$

where:

k_loss,crit is the loss factor associated with the critical pressure, and is based on an average of the forward and reverse loss coefficients.
ν is the fluid kinematic viscosity.
$\bar{ρ}$ is the average fluid density.
D_h is the segment hydraulic diameter, which is the equivalent diameter of a pipe with a non-circular cross-section: $D_{h} = \sqrt{\frac{4}{π A_{f l o w}}} .$ , where A_flow is the Flow area.

Tabulated Loss Coefficient

The loss coefficient can alternatively be interpolated from user-provided Reynolds number and loss coefficient data. The vector of Reynolds numbers can have both positive and negative values, indicating forward and reverse flow, respectively: $k_{l o s s} = T L U (Re) .$

Mass Flow Rate

Mass is conserved through the valve:

${\dot{m}}_{A} + {\dot{m}}_{B} = 0.$

The mass flow rate through the valve is calculated as:

$\dot{m} = A_{f l o w} \frac{\sqrt{2 \bar{ρ}}}{\sqrt{k_{l o s s}}} \frac{Δ p}{{[Δ p^{2} + Δ p_{c r i t}^{2}]}^{1 / 4}},$

where k_loss is the flow loss coefficient, which is selected between the Forward flow loss coefficient (from A to B) and Reverse flow loss coefficient (from B to A) based on the block flow direction.

Energy Balance

The block balances energy such that

$Φ_{A} + Φ_{B} = 0,$

where:

ϕ_A is the energy flow rate at port A.
ϕ_B is the energy flow rate at port B.

Ports

Conserving

expand all

A — Liquid port
thermal liquid

Thermal liquid conserving port associated with the entry or exit port to the pipe segment. Flow is positive from port A to port B.

B — Liquid port
thermal liquid

Thermal liquid conserving port associated with the entry or exit port to the pipe segment. Flow is positive from port A to port B.

Parameters

expand all

Local loss parametrization — Loss factor calculation method
`Constant` (default) | `Tabulated data - loss coefficient vs. Reynolds number`

Method of calculating the pipe segment loss factor. The loss factor is parameterized by either a linear relationship between the segment pressure drop and constant loss factor or by interpolation of user-provided loss factor and Reynolds number data.

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from A to B
`1` (default) | positive scalar

Loss coefficient associated with pressure loss for flows from port A to port B.

Dependencies

To enable this parameter, set Local loss parameterization to Constant.

Reverse flow loss coefficient (from B to A) — Loss coefficient for flow from B to A
`1` (default) | positive scalar

Loss coefficient associated with pressure loss for flows from port B to port A.

Dependencies

To enable this parameter, set Local loss parameterization to Constant.

Reynolds number vector — Vector of Reynolds numbers for tabular parameterization
`[-500, -200, -100, -50, -40, -30, -20, -10, 10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000]` (default) | 1-by-n vector

Vector of Reynolds numbers for the tabular parameterization of the loss coefficient. The vector elements must correspond one-to-one with the elements in the Loss coefficient vector parameter. The elements are listed in ascending order.

Dependencies

To enable this parameter, set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number.

Loss coefficient vector — Vector of loss coefficients for tabular parameterization
`[.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2]` (default) | 1-by-n vector

Vector of loss coefficients for the tabular parameterization of the loss coefficient. The vector elements must correspond one-to-one with the elements in the Reynolds number vector parameter. The elements must be greater than 0.

Dependencies

To enable this parameter, set Local loss parameterization to Tabulated data - loss coefficient vs. Reynolds number.

Flow area — Segment cross-sectional area
`1e-3 m^2` (default) | positive scalar

Cross-sectional area of the pipe segment.

Local Resistance (TL)

Description

Constant Loss Factor

Tabulated Loss Coefficient

Mass Flow Rate

Energy Balance

Ports

Conserving

A — Liquid port
thermal liquid

B — Liquid port
thermal liquid

Parameters

Local loss parametrization — Loss factor calculation method
`Constant` (default) | `Tabulated data - loss coefficient vs. Reynolds number`

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from A to B
`1` (default) | positive scalar

Dependencies

Reverse flow loss coefficient (from B to A) — Loss coefficient for flow from B to A
`1` (default) | positive scalar

Dependencies

Reynolds number vector — Vector of Reynolds numbers for tabular parameterization
`[-500, -200, -100, -50, -40, -30, -20, -10, 10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000]` (default) | 1-by-n vector

Dependencies

Loss coefficient vector — Vector of loss coefficients for tabular parameterization
`[.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2]` (default) | 1-by-n vector

Dependencies

Flow area — Segment cross-sectional area
`1e-3 m^2` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Local Resistance (TL)

Description

Constant Loss Factor

Tabulated Loss Coefficient

Mass Flow Rate

Energy Balance

Ports

Conserving

A — Liquid port thermal liquid

B — Liquid port thermal liquid

Parameters

Local loss parametrization — Loss factor calculation method Constant (default) | Tabulated data - loss coefficient vs. Reynolds number

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from A to B 1 (default) | positive scalar

Dependencies

Reverse flow loss coefficient (from B to A) — Loss coefficient for flow from B to A 1 (default) | positive scalar

Dependencies

Reynolds number vector — Vector of Reynolds numbers for tabular parameterization [-500, -200, -100, -50, -40, -30, -20, -10, 10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000] (default) | 1-by-n vector

Dependencies

Loss coefficient vector — Vector of loss coefficients for tabular parameterization [.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2] (default) | 1-by-n vector

Dependencies

Flow area — Segment cross-sectional area 1e-3 m^2 (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow 150 (default) | positive scalar

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

A — Liquid port
thermal liquid

B — Liquid port
thermal liquid

Local loss parametrization — Loss factor calculation method
`Constant` (default) | `Tabulated data - loss coefficient vs. Reynolds number`

Forward flow loss coefficient (from A to B) — Loss coefficient for flow from A to B
`1` (default) | positive scalar

Reverse flow loss coefficient (from B to A) — Loss coefficient for flow from B to A
`1` (default) | positive scalar

Reynolds number vector — Vector of Reynolds numbers for tabular parameterization
`[-500, -200, -100, -50, -40, -30, -20, -10, 10, 20, 30, 40, 50, 100, 200, 500, 1000, 2000]` (default) | 1-by-n vector

Loss coefficient vector — Vector of loss coefficients for tabular parameterization
`[.65, .75, .9, 1.15, 1.35, 1.65, 2.3, 3.1, 4, 2.7, 1.8, 1.46, 1.3, .9, .65, .42, .3, .2]` (default) | 1-by-n vector

Flow area — Segment cross-sectional area
`1e-3 m^2` (default) | positive scalar

Critical Reynolds number — Upper Reynolds number limit for laminar flow
`150` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.