Computational fluid dynamics (CFD) is the numerical solution of the equations that govern fluid flow. The space the fluid occupies, inside a pipe, around a vehicle or through an enclosure, is divided into millions of small cells, and the conservation of mass, momentum and energy is enforced in every one. The result is the velocity, pressure and temperature of the liquid or gas at every point, plus quantities such as turbulence and the concentration of a gas or particles where they are needed.
Engineers use CFD to answer questions that are hard or expensive to measure: the pressure drop across a valve at its rated flow, how evenly a manifold divides flow between its outlets, how hot a component runs in a fan-cooled enclosure, how much drag a body produces, and where the flow separates or recirculates. Because the whole flow field is calculated, CFD also shows why a design performs as it does, and that is what points to the change that improves it.
The equations CFD solves
For most engineering flows the governing equations are the Navier-Stokes equations. For an incompressible fluid with constant viscosity, conservation of mass and momentum read:
div u = 0
ρ Du/Dt = −∇p + μ ∇²u + ρg
Here u is the velocity vector (m/s), p the pressure (Pa), ρ the density (kg/m³), μ the dynamic viscosity (Pa s), g the gravitational acceleration and t time. Du/Dt is the acceleration of a fluid particle as it is carried through the flow, so the left-hand side is mass times acceleration per unit volume; the right-hand side is the pressure gradient, viscous friction and gravity acting on it. An energy equation is added when temperature matters. These equations have no general closed-form solution for real geometries, so CFD solves them numerically, most commonly by the finite volume method, which balances what flows in and out across the faces of every cell.
What CFD is used for
| Application | What CFD shows | Typical examples |
|---|---|---|
| Pressure drop | The pressure lost at a given flow rate, and which features cause it | Valves, manifolds, filter housings, heat exchangers |
| Flow distribution | How flow divides between parallel paths | Cooling plates fed from one header, air diffusers, burner manifolds |
| Heat transfer | Fluid and surface temperatures, heat transfer coefficients, hot spots | Fan-cooled electronics, heat sinks, cold plates |
| External aerodynamics | Drag, lift, surface pressure and the wake behind a body | Vehicles, drones, wind loads on structures and equipment |
| Rotating machinery | Head, torque, efficiency and the flow through blade passages | Pump impellers, fans, compressors |
| Mixing and separation | Concentration, residence time and particle paths | Static mixers, cyclone separators, dust extraction hoods |
Valve and manifold studies are usually about pressure drop and flow capacity, as in valve simulation. Electronics cooling combines airflow with conduction through the solids, known as conjugate heat transfer, and is the core of electronics thermal management. Pumps are a rotating machinery problem (pump impeller simulation), and the wind load on a structure is an external flow problem.
Laminar and turbulent flow
Flow is laminar when the fluid moves in smooth layers, and turbulent when it breaks into chaotic eddies that mix it vigorously. Which one you have is set by the Reynolds number, the ratio of inertial to viscous forces:
Re = ρVD / μ = VD / ν
V is a characteristic velocity (m/s), D a characteristic length such as a pipe bore (m), and ν = μ/ρ the kinematic viscosity (m²/s). In a pipe, flow is laminar below a Reynolds number of about 2,300 and normally fully turbulent above about 4,000, with a transitional range between.
The numbers show why both regimes matter. Water at 20 °C (ν ≈ 1.0 × 10⁻⁶ m²/s) moving at 1 m/s through a 25 mm bore gives Re ≈ 25,000, well into turbulence. Air at 20 °C (ν ≈ 1.5 × 10⁻⁵ m²/s) at the same speed in the same bore gives Re ≈ 1,700, which is laminar. Thick oils in small passages and slow flows in medical devices are often laminar; most water and air flows in industrial equipment are turbulent.
Resolving every eddy in a turbulent flow is far too expensive for most engineering work, so the flow is solved in a time-averaged form, the Reynolds-averaged Navier-Stokes (RANS) equations, with a turbulence model representing the effect of the eddies. The k-ε and k-ω SST families are the workhorses, and k-ω SST is generally preferred where flow separates from walls or where heat transfer at the wall matters. Large eddy simulation (LES) resolves the larger eddies directly, at much higher computational cost, and is used where the unsteady detail is the point.
Steady-state and transient
A steady-state analysis looks for a flow that does not change with time: the pressure drop through a filter at a fixed flow rate, or the temperatures in an enclosure running at constant power. A transient analysis follows the flow through time, and is needed when the answer itself changes: a valve closing, a tank filling, an enclosure warming up from cold, or a flow that is unsteady even with steady inputs.
Vortex shedding is the classic example of the last case. Flow past a cylinder sheds alternating vortices at a frequency:
f = St × V / D
where the Strouhal number St is about 0.2 over a wide range of Reynolds numbers. Wind at 10 m/s across a 100 mm diameter post sheds vortices at about 20 Hz, which matters if the post has a natural frequency nearby. Transient runs cost more than steady ones because the solution is advanced through many small time steps, so they are used where the time history is the question.
Compressibility is a further choice. Below a Mach number of about 0.3, density changes are small and the flow can be treated as incompressible. Above it, as in high-speed air jets, compressor passages and pressure relief, the compressible form is needed.
What a CFD study needs
- The fluid volume. CFD models the space the fluid occupies, which is extracted from the solid CAD. Inlets and outlets need to be identified, and small features that do not affect the flow can be simplified.
- Fluid properties. Density and viscosity at the operating temperature, plus thermal conductivity and specific heat for heat transfer. Non-Newtonian fluids such as slurries, foods and some polymers need a viscosity model.
- Boundary conditions. A flow rate, velocity or pressure at each inlet, a pressure at each outlet, wall roughness, rotating or moving parts, and fan curves where fans are involved.
- Heat loads and solids. Power dissipated per component, ambient temperature and the materials of any solids that conduct heat.
- Operating conditions. The duty points that matter, including the worst case, and the direction of gravity where buoyancy drives the flow.
- The deciding quantity. Whether the design is judged on pressure drop, maximum temperature, uniformity of flow or force. That choice shapes the whole model.
What the results tell you
CFD produces a complete picture of the flow: velocity, pressure and temperature fields, particle traces showing where the fluid goes, wall shear stress, heat transfer coefficients, forces and moments, and the flow rate through every outlet. The value lies in reading them together. A pressure plot shows how much is lost through a manifold; the velocity field shows that most of the loss happens at one sharp turn, and that a larger radius there would recover much of it. A temperature map shows a hot component; the particle traces show that the cooling air bypasses it through a gap beside a baffle.
Flow distribution problems are typical. A header feeding six parallel cooling channels may look symmetrical on the drawing, yet momentum and friction along the header make the pressure at each branch different. CFD shows whether the split is even or whether some channels are starved, and which change to the header diameter, branch sizes or inlet position evens it out.
What CFD cannot do
- Turbulence models are approximations. Attached flows and pressure drop in internal passages are generally well predicted. Strongly separated, swirling or transitional flows are harder, and the choice of model matters more.
- Boundary conditions carry assumptions. A uniform inlet velocity is not the same as the skewed flow leaving a real upstream bend. If the inlet conditions are wrong, the answer will be too.
- Some physics adds real complexity. Multiphase flow, cavitation, combustion and free surfaces need additional models, each with its own assumptions.
- Each run is one operating point. A pump or fan curve, or a range of ambient conditions, needs a series of runs.
- Testing still has a job to do. CFD narrows the design space so that rig time is spent on the best candidates.
When to bring in a specialist
Building a CFD model is the smaller part of the task. Experience shows in choosing the right physics, the conditions that govern the design and the changes worth trying. A SixGate™ CFD study compares geometries or operating points side by side and comes back as specific changes to geometry, flow path or component choice. Because the study sits inside detail design and simulation, the revised manifold, duct or enclosure can be detailed, drawn for its suppliers and taken into production by the people who modelled the flow. The CFD and fluid dynamics page lists the flows we model.