Orifice Sizing

Orifice sizing to match the flow balancing problem

When designing Thermal Management Systems, a typical problem to solve is the sizing of restrictions on the flow branches to match the desired mass flow rate computed for the cooling of components. This experiment illustrates how this can easily be achieved using the Physics-based Solving capability of Modelon Impact.

Brief summary

This thermal management system is composed of three branches that cool down sets of components. As the amount of thermal power to cool down and a design factor of 30kW/(kg/s) is assumed, it is known in each branch the mass flow rate required to reach a satisfactory design.
Solving this system consists of sizing one restriction per branch to reach the desired mass flow rates in each branch — to satisfy the cooling requirements — and consistent pressure losses across the branches — as these shall match, the branches being in parallel.
Once the sizing problem is solved, the orifices diameters are provided to the model and a small domain exploration is performed on the upstream pressure boundary condition to evaluate the associated mass flow rates in branches.

Thermal Management System of a Hybrid-Electric Commuter Aircraft

The aerospace industry is heavily researching innovative technologies that could reduce its impact on the environment. While disruptive technologies such as hydrogen-power aircraft are being investigated, more incremental ones such as hybrid-electric designs — combining a conventional propulsion system with an electric one — appear as a good first step, providing substantial fuel efficiency improvement, along with gaseous and noise emission reduction.
However, adding the Electric Propulsion System (EPS) does come with a counterpart: it adds direct and indirect weight. The EPS components — batteries, inverters, electric motors etc. — reduce the aircraft payload and need to be cooled down, increasing the weight of the Thermal Management System (TMS). Therefore, achieving an optimized design, when it comes to hybrid-electric aircraft, involves a close coupling between the EPS and the TMS designs.
Several publications address this problem. For our example, we decided to rely on the publication from GKOUTZAMANIS ET AL.: Thermal Management System Considerations for a Hybrid-Electric Commuter Aircraft | Journal of Thermophysics and Heat Transfer (aiaa.org) | DOI: 10.2514/1.T6433

System under study

The following figure, extracted from this article, represents the added network on the TMS and the EPS components to be cooled down:

Figure 1 — Thermal management system architecture

In this TMS architecture, each EPS component is associated with a heat load to be evacuated by the TMS. These heat loads are summarized in the following table:

The assumption is here made that a design factor of 30 kW.s/kg is reasonable for this system. This means, for example, that the right-side branch — that includes both an inverter and an eMotor and thus needs to evacuate 30kW — requires a mass flow rate of 1kg/s from the TMS.

To focus on the problem to be solved, some slight modifications are made to the presented architecture:

  • The pump is modeled with an ideal pressure boundary condition.
  • The heat exchanger is kept outside of the scope of this study — hence substituted by a second ideal pressure boundary condition.
  • EPS components are modeled by pipes and additional pipes and bends are added “randomly” to illustrate the capability of the tool.
  • Flow balancing orifices are added on each branch — these orifices are sized to match the required flow rates.

Solving the flow balancing problem

The added flow balancing orifices — one per branch — shall be sized to match the required flow rates associated with the heat loads to evacuate while ensuring matching pressure drops across the branches. This represents a typical problem to be solved when designing the TMS.
Note that the constraint is a single functioning point and thus results in a steady-state problem. Physics-based Solving (PbS) was added to several LiquidCooling components so that steady-state simulations can be robustly performed. In addition, the LiquidCooling.FlowResistances.Geometric.OrificePlateCircular was enhanced with a sizing capability — which allows the user for specifying a given mass flow rate condition to be matched, from which the orifice diameter will be computed.

This model includes two PbS-enabled experiments in Modelon Impact executed in Steady State mode:

  1. Sizing — which solves the flow balancing problem. The diameters of each branch flow balancing orifices are computed to match the desired flow rate and pressure drops. To use the PbS capability in the components, the boolean parameter settings_TF.usePbS needs to be switched on, and since we are sizing the components, the parameter sizing in the orifices need to be set to true.
  2. Flow Simulation — which has the orifice diameters set to the solution of the flow balancing solution and evaluates different pressure values for the upstream boundary conditions. In addition to setting usePbS to true, we also deactivate the sizing parameters in the orifices and assign start values to orifice openings. The parameter pump.p contains three values ranging from 4.5 to 5.5 bar hence the tool will perform parameter sweeping and execute three simulations in this case.

Results and discussions

The following figure highlights the results of the flow balancing problem by providing a view with the diameter of the orifices to be sized, together with the conditions to be met in terms of mass flow rates, pressures and heat loads.

It can be noticed that the orifice related to the branch that needs to evacuate 10kW is reasonably smaller than the ones related to the branches that need to evacuate 30kW. This is easily explained as the heat load is related to the mass flow rate by the design factor — which is identical here for all orifices.
The orifice in the branch of the generator and inverter is also slightly smaller than the one in the inverter and eMotor branch as the latter branch includes more pressure losses — hence requires less losses generated by the orifice.