## Computational Fluid Dynamics Formulations

We have talked a lot about what we offer in CFD domain. Let’s talk a bit about where these applications are suitable and in this blog we are talking about the computational fluid dynamics. The fluid flow in general can be categorized in multiple ways: steady state vs. transient, single phase vs. multiphase, laminar vs. turbulent, compressible vs. incompressible. Let’s briefly recap these terms from 101 course of fluids.

Steady state flow: A fully developed flow that does not change with time any further. Its equivalent behavior in structural space would be a static model. The inlet and outlet boundary conditions are constant with time.

Transient flow: This flow behavior changes with time. Its equivalent behavior in structural space would be implicit or explicit dynamics. The inlet and outlet boundary conditions may be constant or a function of time or temperature or both.

Laminar flow: A characteristics of a flow governed by a dimensionless mathematical formulation called as Reynold’s number. Usually flows with Reynold number of 2500 or less are considered laminar flows. While we are not discussing quantitative aspects of Reynold number here, all sorts of low velocity viscous flows in contained boundaries are classified as laminar.

Turbulent flow: Flows with Reynold number of 3500 or more can be classified as turbulent flows. Such flows usually have high velocity and low viscosity as well as unstable wall conditions.

Compressible vs. incompressible flow: This is rather a property of fluid instead of property of a flow. Usually incompressible fluids have a well defined constant bulk modulus. Flows with very high velocities in hypersonic and supersonic range have high compressibility.

Single phase vs. multi phase flow: This definition is intuitive. Single phase flows have one or more fluids in a single physical state such as liquid or gas but not both. Multi phase flow state has fluids in multiple physical states such as combination of water and ice at fusion temperature. A composition of two immiscible fluids such as oil and water is still considered a single phase flow.

There is no single CFD solver in the world that can effectively model and solve all types of CFD problems mentioned above. These flows can be categorized in XY graph format as below:

Most of the applications in transportation & mobility, aerospace & defense and Life Science sector fall in category of mainstream CFD. Such flows are steady state, either single phase or multi phase and have a well defined immovable fluid boundaries. Such flows may be with or without heat transfer component. Common mainstream CFD application examples are flow in muffler, electronic assembly cooling, flow in heat exchangers, blood flow in arteries etc. The CFD solver uses Navier Stokes mathematical formulation to solve such problems. It uses conservation equations for mass, Newton’s second law for momentum and first law of thermodynamics for energy. But as we are dealing with fluids, world is not that simple.

There is yet another category of problems outside the mainstream CFD that are very transient in nature. Such problems don’t have a bounded fluid domain. Often fluid domain arbitrarily moves with time. Sometimes flow is multi phase to add further complexity. Common examples of such flow problems are air drag calculation on fast moving vehicle or flying object, design of a waterjet sprinkler, dynamic characteristics of a ship over unsteady water etc. The CFD solver uses Lattice Boltzmann formulation to solve such problems in which fluid is treated as particles instead of a continuum space. However, focus is still on the macroscopic behavior.

There are few other types of flows and formulations as well to model such flows. These formulations are CEL methods, SPH methods and more. If you are looking to solve a specific CFD problem in your organization, we may be able to help.

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