Plenum Inlet - Boundary Condition

Plenum Inlet is a boundary condition that applies an inlet pressure derived from a zero-dimensional model of an upstream gas volume (plenum). It calculates the inlet boundary pressure based on the evolving thermodynamic state (density and temperature) of that volume, which is integrated in time along with the main simulation while neglecting momentum. The plenum itself is driven by a user-specified mass flow and temperature.

A plenum is a large reservoir or chamber with (approximately) uniform thermodynamic properties. In simulations of compressible flows (subsonic or supersonic), one may wish to model an inlet or outlet boundary connected to such a reservoir:

The pressure applied by this boundary condition is governed by the thermodynamic state of the upstream volume. Throughout the simulation, the density and temperature in the plenum are updated based on the net amount of gas in the plenum volume. This net amount is determined by the difference between the flow rate through the boundary and the user-specified supply mass flow rate. The plenum itself is fed with a user-defined mass flow rate and temperature.

This boundary condition effectively blends a pressure inlet condition with a fixed mass flow. When the plenum volume is small, the pressure responds more rapidly to any deviation from the supply mass flow, making the boundary behave closer to a fixed mass flow condition. As the plenum volume increases, it behaves more like a specified pressure boundary.

The expansion from the plenum to the inlet boundary is governed by an area ratio and a discharge coefficient. The area ratio accounts for additional acceleration caused by sub-grid blockages (such as fins), while the discharge coefficient captures the fractional departure from an ideal expansion process.

By design, this boundary condition is intended to be used in conjunction with the supplied mass flow rate. In such a scenario, this BC behaves as a pressure buffer for the incoming mass flow rate.

However, this condition can be also used with flow rate set to 0. In such a case, this boundary condition will represent a pressurized tank which releases gas into the domain. As time will pass by, and the gas will be released, the pressure will drop, until gas stops flowing into the domain.

This boundary condition is well suited for unsteady internal flow scenarios in which a pure mass flow boundary is unrealistic, and a pressure boundary is vulnerable to flow reversal. It was originally developed for simulations of confined combustion.

Plenum Inlet is designed for cases where an upstream gas reservoir (or “plenum”) needs to be modeled by feeding into a flow domain. In situations where a purely fixed mass flow or purely fixed pressure boundary condition is unrealistic—such as unsteady internal flows or confined combustion — Plenum Inlet offers a more physically representative alternative. It allows the boundary pressure to dynamically adjust, according to the state of a zero-dimensional plenum volume, rather than forcing a rigid flow or pressure condition.

The definition of boundary conditions in SimFlow is both simple and intuitive. To specify the Plenum Inlet boundary condition, the user must navigate to the Boundary Conditions panel, select the appropriate boundary for the pressure (either \(p\) or \(p-\rho gh\)) , and choose the correct option from the drop-down menu Figure 1.

The following parameters need to be defined by the User:
Mass Flow Rate \(\dot{m_{in}}\) - mass flow rate into the plenum \([\frac{kg}{s} ] \)
Supply Temperature \(T_{in}\) - temperature into the plenum \([K ] \)
Plenum Volume \(V_p\) - volume \([m^3 ]\)
Plenum Density \(\rho_p\) - density \([\frac{kg}{m^3} ] \)
Temperature \(T_p\) - plenum temperature \([K ] \)
Inlet Area Ratio \(A_{in}/A\) - inlet open fraction \([- ] \)
Discharge Coefficient \(C_d\) - inlet loss coefficient \([- ] \)
Time Scale \(\tau\) - relaxation time scale (optional) \([s ] \)

In this section, we propose boundary conditions that are alternative to Plenum Inlet. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.