It takes many years to earn an engineering degree — but that’s just the starting point. Most professionals spend a lifetime learning engineering concepts and applying them throughout their careers. As you start to go beyond the basic and general concepts to the more specialized areas like simulation, your knowledge and expertise will grow.
However, it’s also not crazy to believe that as an engineer you’ve forgotten more than you remember from your school days. And these fundamentals could become major aspects of your next project.
So, in this article, we want to reintroduce you to some of the ten forgotten secrets and fundamentals of fluid dynamics. This way, you can go from theoretical to practical and effectively set up computational fluid dynamics (CFD) studies using SOLIDWORKS Flow Simulation.
1. Solve some classic fluid dynamics problems
Computational fluid dynamics is the primary focus of SOLIDWORKS Flow Simulation. Think of the cumulative knowledge in your heat transfer and fluid dynamics textbooks. Now package that into a software application that helps you solve real world problems. The software uses numerical methods to solve how your CAD design would react to the flow of fluids around or inside it.
When looking to brush up on CFD, it could be helpful to pull down an old textbook, run some of its problems by hand, and then recreate the scenario to solve it numerically in SOLIDWORKS Flow Simulation so you can compare answers.
2. Navier-Stokes equations are just F = MA
These equations are the starting point for just about all fluid flow problems in college. The Navier-Stokes equations are impressive because they can model literally every fluid on earth. That’s what makes them so impressive — but also what makes them so complicated. They are derived from three fundamental conservation laws of mass, momentum and energy over time and in all 3D directions. The most familiar expression of these is shown below. But to better understand them, it might be best to rearrange them to match the familiar calculation of force equals mass times acceleration (F = MA).
Here’s your guide to deciphering these equations:
The Navier-Stokes equations look scarier than they really are. They are nothing more than Newton’s Second Law, in a per volume basis, over time and in all three directions.
Okay — maybe that escalated quickly. What you need to know is that these are the governing equations for SOLIDWORKS Flow Simulation. Furthermore, using software like Flow Simulation remains the only reasonable way you can solve them in most situations.
The Navier-Stokes equations remain one of the unsolved million dollar challenges from the “Clay Mathematics Institute Millennium Problems.” Thankfully, there’s Flow Simulation to do the heavy lifting for you.
3. Finite volume method is just thousands of little problems
The problems solved by CFD are complicated, so, SOLIDWORKS Flow Simulation breaks it down. When you’re using the software, you’re not just solving one individual problem with your model, but rather hundreds of thousands of little problems.
The technique or process of breaking them down into little pieces is the finite volume method. Each piece is a rectangular parallelepiped — a fancy term for 3D rectangle or rhomboid — with faces orthogonal to the cartesian coordinate system. See a simple example of this below. The Finite Volume Mesh is created for both solid and fluid regions. Each rectangle is known as a cell.
However, this rectangular mesh alone won’t offer enough resolution at the boundary layer (see more on this below) so additional cells are automatically created and solved for internally to account for the complicated things that happen at the boundary layer. After each solid, fluid and partial (both solid and fluid) cell is solved then the results are all “stitched” back together to create a solution. This, in a nutshell, is the numerical technique used by SOLIDWORKS Flow Simulation to solve your problems and provide insight into your designs.
4. Convergence criteria repeating the problem to get the same answer
A converged solution is what we, in CFD terms, would consider the “correct” solution. But there is obviously some nuance to this. as visualized in the image below.
SOLIDWORKS Flow Simulation solves the governing equations (#2) with a discrete numerical technique based on the Finite Volume Method (#3). What’s interesting is Flow Simulation solves the time-dependent set of equations for all problems, including steady state cases. With the numerical method built upon a highly non-linear and transient set of equations, convergence is how we determine if we have the right answer. This works because we’re solving the same problems many, many times with slight changes in mesh and other solver settings. Once we keep getting the same answer iteration after iteration, we have achieved convergence — or in other words, the “correct” answer.
5. Boundary layers and assuming no-slip conditions
You must zoom in many times to see a boundary layer. It’s the very thin area where the fluid meets a solid. It could be anywhere around 1 mm to less than 0.1 mm. This small section has significant effects on the fluid flow and its math is incredibly important. This layer forms because of the no-slip condition which means the velocity of the fluid particles directly at the surface is zero. The velocity then increases as you move away from the solid–fluid interface until you reach the free stream velocity.
SOLIDWORKS Flow Simulation uses a laminar/turbulent boundary layer model known as the “Modified Wall Function” to describe flows in near wall regions. This is an accurate model that can characterize both laminar and turbulent flows near the wall. It also accounts for the transition from laminar to turbulent flow and vice versa.
6. Laminar flow for low Reynolds numbers
Laminar flow is characterized as smooth and orderly. If you look at a laminar fluid flow, you’ll notice it flows smoothly with fluid particles moving in nice parallel layers. Typically, this is low velocity, smaller vessels, and high viscosity fluids. This is visualized in the image above with the yellow lines illustrating the orderly flow. You can quantify laminar flow by calculating a Reynolds number (Re) less than 2,000 — more on this later.
7. Turbulent flow for large Reynolds numbers
Turbulent flow is characterized as chaotic and irregular. Most of the fluid flows in engineering practice are turbulent. If you look at a turbulent fluid flow, you’ll notice there is some irregularity to it with eddies, vortices and significant mixing between layers. Typically, this is high velocity, larger vessels, and low viscosity fluids (air, water). This is visualized in the image above with the pink lines illustrating the “chaotic” flow. You can quantify turbulent flow with a Reynolds number greater than 4,000 (more on this later).
8. Calculating the Reynolds number
The Reynolds number is an important dimensionless quantity in fluid mechanics to characterize the nature of the fluid flow.
Where L represents the characteristic length of the object involved in the fluid flow while the other values are for the fluid like density (ρ), velocity (u), dynamic viscosity (μ) or kinematic viscosity (v).
As we just talked about, the Reynolds number can qualify the nature of the fluid flow as laminar or turbulent. This is because the Reynolds number represents the ratio of inertial forces to viscous forces. With the Reynolds number we can understand when a fluid is laminar, turbulent and even somewhere in between (transitional).
As shown above, when the Reynolds number exceeds a certain critical value, the flow becomes turbulent — in other words, the flow parameters start to fluctuate randomly. What’s great about SOLIDWORKS Flow Simulation is that the complexity of this is all accounted for in the solver. It employs one system of equations to accurately describe both laminar, turbulent and transitional flows.
9. Heat Transfer – Conduction
Let’s add an additional component of fluid mechanics which includes how heat is transferred in solids, fluids and even energy. First let’s talk about conduction, one of the three primary modes of heat transfer. Conduction is the transfer of heat energy through a material (solid or fluid). The heat energy flows from high to low. In simple terms, this can be described by Fourier’s Law which is shown below for a simple solid:
Where q is the heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area of the object and ∆T is the temperature difference. This shows how heat energy flows through the molecules of the medium, whether solid or liquid.
10. Heat Transfer – Convection
Instead of heat being transferred through a material (conduction), convection describes how heat flows between different materials. Think of a kitchen oven, where the hot air (400°F) heats up the solid (chicken or some other food). That’s why your oven is called a convection oven – leveraging natural convection. But, you can take it a step further using forced convection with the addition of a fan to move the air around. It’s the same thing with turning on a fan in your room — it’s not changing the air temperature, it’s just changing the nature of convection, air to skin, to make it feel cooler to you. Making these adjustments changes the heat transfer coefficient shown below as h.
The above equation describes simple convective heat transfer where Q is the rate of heat transfer, h is the heat transfer coefficient, A is the surface area through which heat is transferred, Ts is the surface temperature and T∞ is the ambient temperature.
Computational Fluid Dynamics, revisited
Like we said at the beginning, it only takes a handful of years to earn an engineering degree. But most spend a lifetime continuing to study things beyond the academic setting of school.
In the real world, understanding these complex problems is the key to getting an accurate result. CFD software like SOLIDWORKS Flow Simulation is great at solving these equations behind the scenes. But it’s only as good as the inputs, your inputs, and those are only as good as your understanding of the problem. So, if you want to truly be capable of effectively using a tool like SOLIDWORKS Flow Simulation, you have to make sure you remember the forgotten secrets of fluid dynamics.