Multiphysics Analysis

The ability to simulate the effects of multiple physical phenomena on a digital model helps engineers predict real-world performance

To an engineer, a good design is one that stands up under pressure. Form is important, but function in the face of the forces and stresses an object will encounter during everyday operation is critical.

To evaluate physical models, engineers have long had at their disposal a range of testing methods, such as wind tunnels to assess the impact of airflow through and around an object and crash tests to check for structural validity. In recent years, with the growing reliance on digital prototypes over physical ones, computational testing and analysis methods have begun to supplant, or at least complement, experimental ones. Such numerical simulations, grouped under the broad category of finite element analysis (FEA), can be performed to predict the effects on an object of a range of physical phenomena, including motion, stress, fluid flow, vibration, thermal transfer, chemical reactions, and electromagnetics. As the demand for such capabilities has grown, so has the availability of tools specializing in one or perhaps multiple simulation disciplines.

Electromagnetic and thermal analyses are coupled using Ansys Multiphysics to simulate the real-world stress response of an MEMS (MicroElectrical Mechanical Systems] device. The top image shows contours of generated electric power density. The bottom figur

Until quite recently, however, even the broad-spectrum analysis packages have shared a potentially crippling handicap: the inability to easily couple the results from multiple engineering analyses. This deficiency is significant because, in the real world, individual physical phenomena are often interdependent. The mechanical failure of a part or assembly, for example, is often a function of a variety of forces acting on it.

Consider an electric motor. Not only is it subject to obvious electromagnetic forces when it's in operation, there is also heat transfer due to energy losses. This thermal phenomenon affects the electromagnetic forces, and both could affect the structural mechanics. For example, if the motor gets too hot, it could break. When it's close to breaking, there could be dramatic changes in the electromagnetic state that could cause the motor to stall. Because the physics are mu tually dependent, simulating the effects of each phenomenon independently, without considering the possible interdependence of the others, can compromise ultimate prediction.

To simulate the stirring of molten steel in an induction furnace, engineers coupled an electromagnetics analysis with computational fluid dynamics using Ansys Multiphysics. The software automatically monitors the transfer of the two types of physics data

Coupling multiple analyses, however, has long been considered "difficult physics." While interrelating the results of various physical simulations is not impossible to achieve using traditional FEA tools, the onerousness of the task has often been considered prohibitive, requiring the use of neutral files (which can introduce error) to move data from one analysis program to another, and custom code to enable the data exchange.

Mark Troscinski, product manager for FEA company Ansys, uses an example of a turbine engine simulation to demonstrate the inherent difficulty of solving for various physical phenomena simultaneously. "To determine the pressures acting on the surface of the blade, an engineer might run a computational fluid dynamics simulation. The resulting pressures would cause structural loads on the blades. To simulate the effects of those loads, the pressure values have to be introduced into a structural analysis package."

The structural integrity of a centrifugal pump impeller for a rocket engine depends on the impeller's ability to withstand the airflow pressures exerted on it. Generated in Ansys Multiphysics, these streamlines represent the flow values.

If the displacements of the structure resulting from the fluid-flow pressures are significant-for example, if the air flow causes the blades to bend-the displacement values have to be re-introduced to the CFD software to calculate new flow values based on the updated structural data. To achieve accurate or near-accurate results, the cycle has to be repeated, says Troscinski, "until an equilibrium is reached between the two physics." Solving for the effects of additional phenomena complicates the task exponentially.

Until quite recently, these cyclic iterations had to be achieved "manually." That is, an engineer had to output data from one analysis program, write code to enable the data to interface with another analysis program and vice versa, then move back and forth between programs until a satisfactory result was achieved. As computer-generated part and assembly designs have become increasingly complex, however, the need for easier methods of combining multiple types of engineering analysis has grown, along with engineers' frustrations with the lack of such capabilities.

In response, a handful of vendors have begun developing and marketing tools to ease the pain of coupled-field simulations, also called multiphysics analysis. Though the nature of some of these new tools vary in substance and scope, a common, critical characteristic is their ability to access a broad range of computational analyses capabilities from within a single, familiar interface. "The ability to simulate any number of physics combinations-fluid/structure, fluid/electromagnetic, elec tromagnetic/structural/thermal, for example-from within the same interface, means engineers don't have to move between different analysis programs and they don't have to write their own interfaces to pass the relevant information back and forth," says Troscinski.

To evaluate the chemical process that results from the flow of fluid around a catalyst pellet (fuel element), fluid flow and chemical analyses are coupled in a single, simultaneous simulation using FemLab software.

The various product offerings also share a reliance on the traditional FEA paradigm, whereby a geometric model is subdivided, or meshed, into small elements connected at specific node points, which eases the approximation of stress and strain relationships. Specific information on the material behavior and boundary conditions are attached to each element, providing the necessary parameters for the analyses.

Additionally, the available products in this category all offer standard post-processing, or visualization, capabilities, such as the ability to display velocity vectors, contour plots, and particle traces; zoom into and rotate the models; and generate structural and flow animations.

Though the pre- and post-processing foundations are similar, the products vary considerably in terms of how they integrate the physical analyses that come in between.

One of the first companies to heed the coupled-simulation call was Ansys, with the introduction last year of its Ansys/

Multiphysics product. "In fact," says Tro scinski, "I think we coined the 'multiphysics' label." The software allows engineers to output the finite element model to a special file, called a "physics" file, that incorporates all the characteristics of the type of analysis model to which other phenomena will be coupled. For a fluid/structure interaction, for example, "you would build a finite element model of your structure first and output that model to a structural physics file. Then you'd set up the computational fluid dynamics (CFD) model, put in all the pertinent boundary conditions and fluid properties, then output a fluid physics file for that," says Troscinski. Next, a "solution" procedure is implemented to pass pressures from the flow file to the structural file, and displacements from the structural file back to the flow solution. "It automatically transfers the loads back and forth and monitors the convergence of the different solutions in sequence." This approach automates the communication between the various analysis components, freeing the user from the tedium of trying to achieve the same results manually.

Because Ansys Multiphysics simulations are iterative in nature and rely on separate matrices for each physical phenomenon, absolute physical integration-that which could only be achieved through simultaneous analyses-is beyond its reach. Acknowledging that there is a certain class of tightly interdependent problems for which more closely coupled analyses might be necessary, Ansys is in the process of incorporating a new set of capabilities that combines and solves for the various physical results from within the same matrix. "The new formulation comes directly from the Spectrum product we bought from Centric Engineering," says Troscinski. "It combines the degrees of freedom for the different analyses, which are what you solve for at all of the nodes, into the same element formulation, so there's no going back and forth between the various solutions."

Also on the Ansys agenda are ease-of-use enhancements. "Multiphysics simulation is complicated, especially to an engineer who has a specialty in one area or another, like structural or fluid flow. We're talking about highly nonlinear analysis [the stress/strain ratio varies over time and/or space]. There is not just one physics solution to consider. There may be many, requiring an iterative solution. Our goal is to build-in smart techniques to help the procedure become more robust, more user-friendly," says Troscinski. Ultimately, the goal is to be able to hide the various analyses from the user. "With our DesignSpace product [for linear analyses, in which the stress/strain ratio remains constant or nearly constant], we can tell the code: 'This thing is made out of aluminum,' then push a button to find the answers. Under the hood, it does a finite element mesh, solves the problem, and then reports the results. We want to be able to get these very sophisticated nonlinear ca pa bilities to be as easy to use as the linear stuff."

Structural and flow analysis generated in Algor were employed to determine the resultant forces from flow around this turbine. Once calculated, the flow forces were projected onto the object for a structural analysis. To compensate for the displacement ca

The company also plans on adding more physical ca pa bilities-among them, the ability to generate CFD calculations for free surfaces, such as those encountered between liquid and air in some type of container, where the shape of the liquid surface is dynamic. In such cases, says Troscinski, "you're trying to predict the shape of that surface as a function of time. We want to be able to automate the solution for these kinds of things."

An unsteady fluid flow analysis simulates the effects of gravity when water drains in a sink. As the sink drains, turbulent eddies form above the drain hole. The two views of the analysis model show real areas of relatively high velocity in the middle of the sink. Using the coupled-physics capabilities built into Algor software, engineers can merge CFD analysis results such as these with those of interrelated physical simulations, including heat transfer and stress, to better approximate reality.

Another multiphysics approach being taken by some companies is to provide specialty programming tools that let users, within a single interface, link the capabilities of various analysis modules by writing macros defining specific physical couplings. FEA veteran Algor uses this approach. While Release 12 of the company's analysis product line has automated capabilities built-in for the more "common" couplings, a special programming language called Eagle can be used to solve complex multiphysics problems, accord ing to Robert Wil liams, development di rec tor at Algor. "One of the most common multiphysics applications is thermal/ stress analysis, where temperatures are applied to either a linear static or nonlinear static model to solve for the stresses caused by that temperature. To get the temperatures, an engineer can set up a heat-transfer model, run the analysis to find the unknown temperatures, then the software can automatically apply those calculated temperatures back to the model to get the appropriate stresses."



Nonlinear dynamic calculations in which the values change as a function of time are not as straightforward. For example, notes Williams, "you could have a situation where the heat transfer is affecting the flow of a fluid, changing its viscosity or flow speed. But also, that fluid is flowing over some structure, putting forces and pressures on the structure. You basically have a need for a heat transfer/fluid flow/structural analysis bundled into one, where it's not as straightforward as to what output you want to look at from one in order to vary the input for the next."

In such a scenario, the engineer can create a macro in Eagle that tells the program what to do in between each of the analyses. "The thermal results may change the viscosity of the fluid, for example. You can write code that knows how to read our result files and manages the interchange be tween them. You can program it to change the viscosity in the thermal model, and then run the fluid analysis and look at, perhaps, a resulting pressure distribution from the fluid flow analysis. Based on that distribution, it will put forces on your linear static stress model," says Williams. "Basically what you're writing is the logic between these different analyses to read the results of each." The macro can than be programmed in an iterative loop bounded by some final parameter that represents the specified design criteria.

The key to the success of this approach is an awareness on the part of the engineer of the physical phenomena that are acting on a given part in order to properly set up the models and determine the order in which the analyses should occur to reach the desired solution. Realizing that this isn't always the case, Algor is working to broaden the automated capabilities to minimize the need for creating macros. Eventually, the company hopes to enhance the product line so the user can, within a single model, set up loads and constraints for the range of analyses to be run.

Particle traces generated in Ansys Multiphysics illustrate the flow of blood in an MEMS microfluidic channel in a medical device. The flow forces can serve as input to other physical simulations to predict the real-world success or failure of the device.

"We want to get away from the whole concept of: 'I'm building a heat transfer model or a fluid flow model,' and get more in the mindset of "I'm designing a part and many things are affecting it.' Maybe there's some temperature, maybe there are some forces," says Williams. "From an analytical side, that means considering heat transfer and linear static stresses. From the user's perspective, all he or she wants to do is put in temperatures and forces. Eventually, using a single model, a user will be able to say, 'run analysis type 1, run analysis type 2,' to get to an optimal design."

A new product from a Swedish company called Comsol brings multiphysics modeling close to that ideal. Called FemLab, the analysis program runs on top of MatLab technical computing software (The Math Works; Natick, MA) and enables the direct manipulation of partial differential equations (PDEs)-mathematical des crip tions of physical phenomena. The software lets users model any number of physical phenomena simultaneously. Unlike most other analyses packages in which PDEs governing the range of physical properties are hard-wired and thus untouchable by the user, FemLab lets engineers explicitly set up, manipulate, and solve individual PDEs as well as coupled systems of PDEs. Through this approach, a single set of solvers is employed to generate solutions, regardless of the discipline. Because of this, says Bjorn Sjodin, development group leader at Comsol, "we can solve just about any multiphysics problem using any kind and number of physics phenomena."

Unlike the iterative approach to achieving coupled results, the single-solver PDE approach enables a "true" simulation of real-world performance because the solutions are not achieved sequentially and then fed back into another type of analysis, but rather are simulated simultaneously. "Each PDE defines one kind of physics. For solving coupled physics problems, you need to solve coupled systems of PDEs. If you are not able to simultaneously solve these coupled systems, you are forced to put a sequence of single-physics problems in a loop, hoping for the whole process to produce a solution," says Sjodin. "This typically cannot be done for real-world problems, especially those that involve nonlinear physics, which are ubiquitous."

One disadvantage to this approach, however, is the requisite computational demand. "Because we're solving these true coupled physics problems that no one has solved before, there's a higher demand on the numerical analysis component," say Sjodin. "You get new numerical effects for each coupled physics phenomena that you want to model, and each coupled phenomena gives a new numerical problem. As a result, we have to prepare our products for this general kind of modeling."

Because of this, the current version of FemLab is limited to analyzing two-dimensional physics problems. "We solve problems in a single plane. For example, if you want to look at the water flow in a tube, then you can take a cross section of the tube and watch that single part," says Sjodin. But if the tube is an irregular form, if it's something that has indents and bump-outs, a 3D representation is crucial. "In such cases, it isn't enough to take a cross section at one place. You need to model the entire 3D shape to be able to get the accurate physical simulation." Thanks to advances in computational power on the PC, a 3D version of FemLab is slated for release later this year.

As engineers begin to get a taste of how multiphysics analysis capabilities can make their jobs easier, their demands for such tools will no doubt send FEA vendors back to their drawing boards to come up with bigger, better products. The availability of enhanced multiphysics capabilities in some of the existing FEA products have already upped the ante for other FEA companies to shore up their coupled-simulation offerings. Analysts agree that it will no longer be enough to throw a common interface over a collection of different legacy codes and solvers without truly integrating the technologies. To compete, FEA vendors will have to come up with their own unique, powerful ways of bringing together the range of real-world phenomena that "in-service" parts and assemblies are subject to.

Diana Phillips Mahoney is chief technology editor of Computer Graphics World.

The following companies offer products that provide access to broad-spectrum analysis capabilities, which can be coupled automatically or through custom programming to achieve multiphysics simulations. The list is not exhaustive, nor does it include shareware tools or commercial tools that specialize in only a subset of the full range of analysis types.

Pittsburgh
412-967-2700
www.algor.com

Canonsburg, PA
724-746-3304
www.ansys.com

Burlington, MA (US subsidiary)
781-273-6603
www.femlab.com

Los Angeles
323-258-9111
www.mscsoftware.com

Los Angeles
310-207-2800
www.srac.com