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Fluid dynamics: simulation of an oil system

  1. Sep 3, 2017 #1
    Good day folks!

    I am working on the simulation of an engine, and in particular the oil system makes my head ache. I already finished the calculations for viscosity and temperature, but now I'm stuck on coming up with formulas for pressure and flow rates. With what should I start?

    For simplicity let's say the system consists of the following components:
    1. an oil tank or sump
    2. an engine-driven oil pump
    3. the lines and crevices of the engine

    Here's part one of the problem:
    I'd say the starting point would be the pump, because it is the pump that sets everything in motion. BUT what does the pump actually do? Is the pump generating a pressure between the inlet and the outlet, which then generates the oil flow? Or is the pump generating a flow which results in a pressure differential?

    Part two:
    Since the oil is pretty much not compressed in any meaningful way, I assume that the volume of oil that enters the system is the same as the volume of oil pushed out of it, back to the sump/tank. But how do flow and pressure change when the oil is, for example, pressed through a tiny hole? The pressure rises in front of the hole, it decreases behind the hole. But that also means that there's a big pressure build-up right after the pump, right?

    I'm very confused about the relationships between all these variables, and even after reading up a lot on fluid dynamics, I'm still in the dark putting everything into practice. I'd love to hear your thoughts, and hope you can point me in the right direction.

    Thanks a lot!

  2. jcsd
  3. Sep 4, 2017 #2


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    Welcome to PF.
    Potential energy is added to the fluid by the pump. The pressure of the fluid increases as it flows through a pump. There will be a pressure regulator that limits maximum pressure. Rate of energy flow = power = flow rate * pressure difference.

    A pipe or orifice costs pressure, which is determined by flow rate. It is not linear. There are a few chapters on fluid flow there for you to study. You will need to identify different types of equations, dP = f ( flow ), for each type of obstructive channel.

    Draw up a mesh “circuit diagram” for oil flow. You will need to solve it using Kirchoff's laws which involve equations for the pressure at nodes and oil flow between nodes.

    I would draw the flow diagram, with node pressures as the state variables. Guess initial pressures, then relax them as you recalculate flows needed to get the flow into each node = flow out of that node. Once the computation stabilises it will give values for all flows and all node pressures.
  4. Sep 5, 2017 #3
    Thank you for your input! Looking at this problem from a perspective of power is a really good idea. This way I could actually integrate the heat exchange in the equations as well.

    However what I am hoping for is a more modular solution in general. So rather than looking at the whole mesh, I'd like to break it down into it's components, pass relevant data of the connected parts and solve for pressure individually. Since this is a continuous simulation it should bear good results that way as well I believe. Is that feasible? And if so, what would be the relationship between the outgoing pressure of one component to the pressure of the receiving component. I.e. how does the pressure interact?
  5. Sep 5, 2017 #4


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    Not normally an actual cross connected mesh in normal engine designs . Most commonly the oil flow paths are in form of a tree with spreading branches . Analysing an oil flow system in detail is always going to be difficult but it will be relatively much easier for a tree than for a mesh .

    Very much simplified :

    Pump takes oil from a sump and causes it to flow into a primary distribution duct .Smaller branch ducts and secondary branch ducts guide the oil to the several places where it is needed in the engine . At the delivery points at the ends of the branch ducts there are usually nozzles .

    With a positive displacement pump the total volume flow rate and total mass flow rate of oil will be nominally fixed at any given engine rpm .

    The flow area through all the nozzles taken together controls the pressure that has to be generated by the pump and the relative sizes of the nozzles in different places controls how much oil is delivered to each place .

    Oil returns to sump by gravity flow .
  6. Sep 5, 2017 #5


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    An energy audit is a better description. With lubrication you can usually ignore the fluid mass, gravitational potential energy and the kinetic energy of the fluid. Instead you have pressure and volumetric flow.

    You build the mesh from all the modules. If at low RPM the oil flow needed by all modules exceeds the pump flow, then some pressures will fall. That requires you model a complete system and not just one little corner. You will also need to find the viscosity temperature relationship for the oil. When the sump oil temperature rises most components will behave slightly differently.

    The pressure drop across a lubricated bearing will heat the fluid in proportion to the flow. Since radiation is involved you can expect to have a thermal energy flow diagram that is expected to be slightly more complicated than the hydraulic diagram.

    Pressure drop is usually an interesting function of flow rate. When you connect two components in series, the flow is the same in both, but the pressure drops add to the total pressure. In parallel the flows are added but the pressures are the same.

    Start by drawing a picture of all the flows, passages and restrictions.

    Flow into the crankshaft feeds a number of bearings which needs to be modelled as a ladder network. A mesh is a matrix, which may be sparse, but it is the general solution for a system or network of trees and ladders.
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