Coupled simulation provides multi-domain analysis of thermal, mechanical and electrical performanceBy Bogdan Ionescu and David Vye, Ansoft Corporation

Product reliability has long been the concern of the aerospace and medical industries where failure in the field can

have catastrophic consequences. These products must demonstrate readiness to operate under the harsh conditions of extreme temperatures and/or power levels without serious performance degradation. In the past, accessing the reliability of a particular component has been the responsibility of the design engineer working closely with specialized test engineering to replicate realistic field conditions. This approach is costly, extremely time consuming and prone to inadequate identification of likely failure mechanisms.

Recent developments in simulation technology now allow engineers to investigate the cause of component breakdown as it relates to heat, stress and exposure to excessive power. By coupling thermal, mechanical and electrical analyses into a multi-domain simulation, the inter-relationships between these properties can be accounted for. This article examines how these coupled technologies work; how they improve simulation accuracy and some of the applications where multi-domain analysis makes a comprehensive reliability study feasible and practical.

Underlying simulation technologyTo address multi-domain analysis, the ePhysics simulation software from Ansoft Corporation couples thermal and stress analyses to the electromagnetic simulators, HFSS and/or Maxwell 3D. HFSS is a 3D full-wave Finite Element Method (FEM) electromagnetic simulator which computes electrical behavior such as S, Y and Z parameters for high-frequency and high-speed components. Maxwell 3D uses 3D Finite Elements to compute the transient, AC magnetic, DC magnetic, and the electric fields of low-frequency components. Together, these EM simulators provide the electrical behavior that dynamically co-simulates (via datalink integration) with the thermal and stress solvers in ePhysics to replicate the true nature of the device physics. The data flow between the two EM simulators (HFSS and Maxwell 3D) and the thermal and stress solvers in ePhysics as shown in figure 1.

The thermal analysis in ePhysics solves the nonlinear steady-state and transient thermal behavior of a device, including all heat transfer mechanisms: conduction, convection and radiation. In a typical multi-domain analysis, designers may use power loss and core-loss distribution information obtained by the electromagnetic field solver as a heat source for thermal analysis to obtain a complete thermal profile of a device, including overall temperature distribution and location of hot and cold spots for any instant in time. Furthermore, temperature distributions can be channeled into an elastostatic solver to evaluate the induced mechanical stress and resulting deformation.

The Data link automates various mechanisms to support simulator coupling for multi-domain analysis. Key functionality performed by the datalink includes:

— import a starting mesh from the coupled simulator of any eligible design (designs must share a common geometry);

— import the initial temperature distribution from a static thermal solution (if thermal transient solution is used);

— usage of adaptive mesh refinement (ensures the mapping of the applicable fields and automatically monitors between different meshes in the coupled designs); and

— automatic mapping of parameters between coupled designs.

Creating datalink coupling between two solvers is generally a two step process namely, design generation and simulation set-up. In a typical use case where an engineer is investigating temperature distribution related to current losses, the ePhysics thermal solver must be linked to HFSS. To create a link between ePhysics’ thermal solver and an existing, pre-solved HFSS project is simply a matter of selecting and copying all objects in the HFSS “source” design into the ePhysics “target” design, selecting the desired type of solution for the design and adding the appropriate boundary conditions, sources (other than those of electromagnetic nature which are set by HFSS), and establishing the datalink between solvers. The datalink between solvers is easily established by specifying the project location, as well as the design and solution setup involved in the coupling as shown in the datalink set-up panel in figure 2.

The dynamic datalink allows parameters to be shared between coupled designs. For example the magnetic biasing current parameter defined in the magneto-static solver (Maxwell 3D) can also define a parameter sweep in HFSS or in the ePhysics’ stress analysis setup. Thus the whole range of simulations in Maxwell, HFSS and ePhysics are performed synchronously and the results of the parameter sweep are available in the post processor for viewing without any additional intervention from the user. Figure 3

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Figure 1: Data flow between four solvers: Maxwell, HFSS, ePhysics Thermal, and ePhysics Stress.

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illustrates the family of curves reflecting the power loss in the circulator due to the high frequency fields and the influence of the magnetic biasing current.

To demonstrate the datalink, coupled simulation and multi-domain analysis; a ferrite circulator is fully examined with all four of these simulators. The complex simulation will center around high frequency electrical characterization by HFSS which is dynamically coupled to a non-linear magneto-static solver (Maxwell 3D) for capturing the biasing fields distribution in the ferrite and also to the thermal and stress solvers in ePhysics for evaluation of other consequences of these high frequency fields namely, the temperature distribution and thermally induced stress throughout the circulator.

Non-linear ferrite characterizationThe ferrite circulator is a three port device using a transversely magnetized ferrite which is responsible for directing the flow of microwave energy from port A to port B, port B to port C and port C to port A (figure 4). The non-reciprocal nature of the device

essentially prevents power flow from port B to port A. This component is widely used in many microwave/RF applications to channel the flow of microwave energy in a specific direction as required by the system. Circulators are most often located between the transceiver’s power amplification stage and the radiating antenna, where the highest levels of microwave energy occur and components are particularly susceptible to high currents and elevated temperatures. Therefore, simulating the multiple physics interactions is critical to understanding the magnetic biasing field, the resulting RF electrical performance and the thermal and mechanical consequences of exposure to these high frequency electromagnetic fields.

A ferrite’s permeability tensor is the direct result of an applied static magnetic bias field requiring a non-linear magneto-static solver such as Maxwell 3D to simulate. However, the microwave circulator in which the ferrite is used requires a full-wave high frequency solver

such as HFSS. Improper accounting for the distribution of the non-linear magnetic fields inside the ferrite reduces the accuracy of the overall device simulation. With dynamic co-simulation, HFSS can incorporate a Maxwell 3D simulation of this static magnetic biasing field within a high frequency simulation of the circulator, accurately capturing the non-linear behavior of the ferrite. Thus the datalink allows the low and high frequency simulators to share data, eliminating the use of a uniform bias field approximation and increasing the accuracy of the electromagnetic solution accordingly.

EM/transient thermal co-simulationWith the non-linear ferrite behavior incorporated into the electrical characterization of the circulator via the datalink between HFSS and Maxwell, the designer can now investigate the thermal and stress consequences of the power loss distribution. The power loss distribution corresponding to the power loss peak can be channeled to ePhysics from HFSS for simulation of the transient temperature evaluation and the stress and deformation at user-specified moments and corresponding temperature distributions as shown in figure 5.

If a thermal transient solver is used, the following formulation exhibits some of the features available in that solution sequence.

In the formulation above Qv represents the power loss distribution, k is the thermal conductivity tensor, is the mass density, c is the specific heat. The thermal diffusion equation is solved subject to initial temperature distribution throughout the model (see equation below) and to user specified boundary conditions.

Figure 2: Datalink setup panel.

Figure 3: Frequency and biasing current sweep results.

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Figure 4: Power flow in a non-reciprocal ferrite microwave circulator.

Figure 5: Scaled thermal deformation of the device at user-selected moments.

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Free and forced convection and thermal radiation effects can be included in the model using advanced convective and radiative boundary conditions.

The datalink setup supports HFSS arbitrary excitation sequencing such that an arbitrary sequence of power pulses can be efficiently generated to create the desired ePhysics input as a function of time, based on a single HFSS solution. The corresponding results are easy to extract. The user definable parameter setup allows the thermal solver to calculate global quantities such as object-wise average temperature, hot spot and cold spot temperatures and their respective locations.

Additionally, field distributions and other calculations can be performed using post processing, figure 6.

During steady state or transient (pulsed) operation, high temperatures can result in the device. In cases like this, forced convection is often used in real life applications to cool down the device. A structure with forced cooling can be simulated in ePhysics via the dedicated forced convection and radiation boundary conditions. The operation using forced convection is reflected in the model featuring user-specified convection channels which allow the flow of a variety of cooling fluids at specified velocity. Figure 7 presents the modified device with cooling channels located in the walls of the waveguide structure.

The setup of the forced convection on the walls of the channels allows the user to choose among a few available fluids or specify newly defined ones. The setup also allows the specification of all needed parameters for flow inside the ducts if necessary (figure 8).

The datalink setup may be used to investigate a wide range of device performance metrics. For example, assume that the effect of submitting the forced convection circulator to low temperatures without high frequency power needs to be investigated. In this case the effect of the “cooling fluid” can very well become a heat source if the temperature of the fluid is above that of the low ambient temperature. Figure 9shows the transient response of the average temperature of the ferrite part with an initial temperature of 0 °C under the influence of the fluid flowing in the respective channels.

EM/transient thermal co-simulationThis article presents the interactions between the electrical, thermal and mechanical behavior of a typical microwave/RF component and how the recent linking of dedicated simulators is allowing engineers to investigate the true nature of the hardware they are developing. Due to the dynamic nature of the data link between these simulators and the possibility to map parameters between solvers, the usage of electromagnetic setups results becomes readily available to users interested in exploring the thermal and mechanical effects of electromagnetic devices.

This new capability is especially important to designers of high reliability products such as those in the areas of antennas, microwave components and devices, high speed connectors, bio-medical and aerospace applications where replicating field conditions in the lab is particularly costly and difficult.

Figure 7: Geometry of the device with cooling channels in the walls of the waveguide.

Figure 6: Thermal and stress post-processing results:- a) deformation, b) temperature distribution, andc) thermal transient response reflecting excitation sequence in HFSS.

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Figure 9: Transient response of the average temperature of the ferrite part.

Figure 8: Forced convection parameters setup panel.

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