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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.
  7. Dec 3, 2017 #6
    Hello folks,

    sorry for the late reply. In all honesty I was a bit discouraged from your last response. I was initially hoping to find a simple, modular, out-of-the-box solution. Since there's no such thing, I decided to focus on something else in the meantime. But it's time to get back to my oil system and I did think a lot about it and would love to hear what you think about my thoughts.

    First off, my knowledge of fluid dynamics is somewhat limited, however I feel very comfortable in the realm of electrics/electronics. From what I understand, this problem is very much like an electrical circuit. Is it fair to assume that similar correlations can be drawn?

    I did draw the mesh of the oil system (Sorry for my bad penmanship:biggrin:):

    I identified the following components, starting top right:
    The oil tank T1 connects though oil line L1 first to the oil pump P1 and then to the filter/screen. Oil line L2 gets the oil to the engine, and there are five components R1-R5 before the oil gets collected in the sump T2.
    The red spots mark the different pressure points and blue is the oil flow.
    I skipped the return path, since it's more or less independent from the oil flow through the engine.

    I did the calculation for the viscosity, based on oil grade and temperature.

    The way I would approach this problem in electronics is to calculate the "resistance" in each component as a division of viscosity and the area cross-section of the component (something like: R=VI/A). I can then substitute the complex mesh with simpler ones with this:
    Rtot=R1+R2 for serial connections and 1/Rtot = 1/(R1+R2) in parallel connections.

    The oil pump can be either be seen as a PRESSURE generator.

    This is where the analogy to the electrical mesh ends though, since in electrical systems you always have closed circuits in which the sum of all voltages equals zero. In the case of my oil system I end up with a mesh consisting of a tank, a pump, a "resistor" and the sump. The flow rate must then be calculated from the pressure generated by the pump against the total resistance.

    So here are my updated questions:
    1. Are my assumptions more or less correct? If so:
    2. What physical property is the "resistance" and what governing formulas exist for them?
    3. What would be a formula for my last step? I.e. How do I calculate my flow rate in this simplified mesh?

    Thanks for you patient, you have been a great help!!
  8. Dec 3, 2017 #7


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    The analogy of an electrical circuit is a good start to working out the diagram. But it gets more complex very quickly because the resistance to fluid flow through an orifice is not linear like a resistor.

    The use of fluid lines are more critical with hydraulic systems than are wires with resistors. Hydraulic lines behave more like electrical transmission lines.

    The analogy of the return circuit is present in fluid flow, the many returns to the tank or sump is the equivalent of the common ground or earth connection.

    You must decide when a fluid flow switches from a laminar flow model to a turbulent flow model. The following is essential reading. https://en.wikipedia.org/wiki/Darcy–Weisbach_equation

    I do not think you can proceed without some graphs of flow versus pressure for the components of your system. You might compute those initial relationships, but I would be happier to experiment with hydraulic oil, differential pressure gauges and an accurate variable flow pump. I have a couple of tonnes of parts that I play / experiment with. That way I know what is real.

    Maybe you could adapt an experimental motor to have multiple lubrication flow and pressure test ports.
  9. Dec 3, 2017 #8
    I'd love to run those experiments, but the engine I try to simulate would set me back about 8000 Euros. I have to resort to assumptions and estimations for my parameters.

    It's a continuous real-time simulation and it's not so much about the precision. If my simulation has the ballpark figures right, I'm happy enough. The main goal is to be able to simulate a realistic response to different boundary conditions. For instance I want to see a high oil pressure when the engine is starting at -20 degrees. Or a drop in pressure if a pipe starts leaking. Ultimately I want to come up with the formulas for the entire oil system first and then fine tune the parameters of each module by trial and error until I get a model that more or less reflects a realistic behaviour. So, the parameters don't really matter as much, what's important is to get the correlations right! Also, I want to limit the calculations to laminar flow only.

    I skipped the return flow above, simply because it is completely detached from the rest of the mesh. That is because in this case the oil tank and the sump are two separate components. The oil drips and squirts into the sump, which acts as a reservoir. From there a secondary pump is pumping the oil back into the main tank.

    OK, from what I'm getting, this is the course of action:

    1. Calculate the energy that the pump is putting into the system - the energy is a function of the RPM of the engine and factors such as the efficiency.
    2. Calculate the pressure loss for each component using Darcy-Weisbach with viscosity, pressure and geometry as input values.
    3. Sum up the pressure loss in the entire system
    4. Calculate the pressure of the pump as a function of the pump's energy and the pressure loss of the components.
    5. Calculate the oil flow as a function of the pump's pressure, it's energy and the oil's viscosity.
    6. Calculate the oil flow and pressure of each component
    7. Rinse and repeat.

    Does this sound about right?
  10. Dec 3, 2017 #9


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    That sounds like a good plan.
    Don't forget the oil pressure relief valve and the backflow leakage of the pump. The oil grade, age and temperature will give a wide range of viscosity, so you must select and compute maximum and minimum viscosity values for the model.
    How will you model a blocked oil filter with cold oil, does the filter have an internal bypass valve?
  11. Dec 3, 2017 #10


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    Just to make it explicit for others reading this thread.

    Real World engine oil pumps are, as @Nidum stated in post #4, positive displacement pumps (Gear Pump). That is, at any given speed they will have a specific flow rate proportional to speed, regardless of pressure, until something breaks. They are followed by a (usually built-in) Pressure Relief Valve at the pump output to dump the excess volume of oil. This way the available pump outlet pressure is limited by the Relief Valve pressure setting, the valve size, and the oil viscosity. Older automobiles had an oil pressure gauge on the dashboard that usually read 40psi during cruising, but would often read lower at idle, especially in worn-out engines. Present day engines probably run at a higher oil pressure, needed to get oil into bearings operating at higher loading.

    EDIT: I see Baluncore just beat me to some of this as I was typing.
  12. Dec 3, 2017 #11
    There is a pressure relief valve on the primary pump, which activates a by-pass back to the oil supply line. That should be easy enough to implement, since the opening of the bypass is a simple function of the output pressure of the pump. The oil filter itself doesn't seem to have a bypass though.

    Oh man, that's interesting! We are talking about a gear pump here. The thing I'm wondering is how reliant the "constant flow" is when you operate it outside the norm. Let's say you're starting the cold engine at -20 degrees and your oil is already a bit old (Mind you: mineral oil, no additives!). I'd say there are two things that could happen: If the oil pump really displaces oil at a constant rate (only proportional to the rpm) the pressure would just build up until the bypass valves up. I could also imagine that oil that sluggish won't be displaced by the pump anymore, since it's not really liquid anymore. In this case the gears of the pump would simply rotate the same chunk of oil-goo round-and-round. So, the oil pressure would stay rather low, while your engine is slowly grinding down every single moving part until it breaks. :biggrin:

    Also consider the opposite case: if your engine is running extremely hot so that the viscosity of the oil is waaaaaay below the normal operating range, the gears of the pump can't "grab" the oil anymore. It's just too thin. In this case the oil pressure again would be rather low with even worse results (since the engine is already running hot).

    This is why I was thinking of having the pump produce pressure, rather than flow. But I'm happy to hear a counter-argument.

    Thanks for your responses guys, you help me lots!
  13. Dec 3, 2017 #12


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    Take an oil filter apart to see if there is a spring loaded plate. You would be surprised by what there is hiddden in a filter. The more it costs the more likely there will be a bypass.
    Two interlocking gears will pump a fixed displacement on the outer part of both gears. The middle return is blocked by the meshing teeth. If they cavitate then it will be because the filter is blocked or the engine oil is jelly which will show in your simulation. Tip and face clearance in the pump allows some backflow which limits maximum pressure with low viscosity hot oil at low RPM.

    Almost all hydraulics is flow based which is quite the opposite of the electrical analogy. Pressure only occurs when the flow is obstructed. It leads to economy because flow * pressure is power. Engine lubrication is slightly inefficient because it always has flow and pressure.
  14. Dec 3, 2017 #13
    What are the specifications of the oil filter used in your simulation? Spin-on automobile engine filters have an internal pressure relief triggered by excessive differential pressure to prevent element collapse, and allow (unfiltered) oil flow if the media becomes clogged. Unfiltered oil flow isn't desirable, yet isn't as catastrophic as no flow (and not long afterward, a seized engine), or having the element break apart, and spew debris into the oil.

    This differential bypass is built into the filter (or perhaps into the filter head, although I've only seen these in hydraulic systems), and is in addition to the high pressure relief connecting pump outlet to sump.
  15. Dec 3, 2017 #14
    I see @Baluncore posted an answer to the filter bypass issue. Forgot to add it to the previous post, but when doing a cursory check for auto oil filters without an internal bypass hit upon this informative engine oil filter study you may also find interesting.
  16. Dec 3, 2017 #15


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  17. Dec 3, 2017 #16
    In a positive displacement pump such as a gear pump, whatever makes it into the pump must come out the other side (minus back flow past gear tip and face clearances as @Baluncore pointed out, as well as side plate clearances). Very cold, highly viscous oil may not flow into the gear mesh at all, or at a rate lower than what the pump tries to take away (in which case the pump cavitates).

    Unlike a centrifugal pump, oil within a gear pump cannot run around in circles - it shows up at the outlet, flows through the clearances, or develops enough force to blow the seals or break something else. Clearance back flow is viscosity dependent, and is lower for cold, high viscosity oil than when oil is hot and thinned out.

    If it enters the suction port that hot oil is going somewhere. Very hot oil has an easier time of it going past clearances than when at normal operating temperature, but (unless the pump is badly worn) most of it still shows up at the pump outlet. Most of my oil gear pump experience was with force lubricated industrial gearboxes, and the following chart isn't directly applicable, but my suspicion is engine mineral oil viscosity curves flatten out in a similar manner as temperature rises as do these for PAO synthetic oil.

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