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Bernoulli Equation
ReStackor pro Fluid Dynamics
ReStackor uses fundamental fluid dynamics to accurately compute flow through the clicker bleed circuits
The Bernoulli equation computes the forces required to accelerate a fluid through a flow restriction. This basic fluid dynamic equation is derived from Newtons fundamental equation:
For a fluid flow the force is the pressure time the area (F=PA), the mass is the fluid contained within a small axial slice of the flow (m= rho A dx) and the acceleration is the change in fluid velocity (a=du/dt). With these definitions Newtons equation becomes:
Bernoulli Equation Developed in 1738
For flow from a reservoir into an orifice the initial velocity is zero (u[1]= 0). With this substitution the above equation becomes:
This is the well know Bernoulli equation developed in 1738. The equation relates the flow velocity to the pressure drop required to establish that velocity. For a suspension system this equation is more intuitive written the other way:
The pressure forces generated by a shock absorber are proportional to the velocity squared. If you hit a bump that causes the suspension to move twice as fast the pressure resistance through an orifice increases by a factor of four. This rapid increase in pressure for small changes in velocity is why shock absorbers use a shim stack to control the valve flow area. At high velocities deflection of the shims increases the available flow area through the valve. The larger flow area reduces the flow acceleration required for the flow to pass through the valve gap. This keeps the pressures from spiking within the shock absorber.
Through control of the shim stack stiffness you control the damping forces produced in the shock absorber.
Viscosity effects
Flow approaching an orifice along the centerline flows directly in, flow approaching from the side has to turn into the orifice throat. Turning of the side entrance flow bends the streamlines and creates velocity gradients across the flow. The velocity differences in these streamlines generate shear forces as the high velocity centerline flow tries to drag the lower velocity perimeter flow along with it. While these forces are small it is these shear forces that create the differences in the flow resistance when you change from 5wt to higher viscosity 10wt oil.
High oil viscosities increase shear losses in orifice entrance flows.
The bending of the streamlines at the orifice entrance also creates a fluid dynamic flow restriction in the throat of the orifice entrance. The low velocity side entrance flow is still turning as it enters the orifice. This creates a restriction and an “effective” flow area that is smaller then the geometric area of the orifice. The amount of restriction is dependant on the flow velocity, fluid momentum, entrance geometry and viscosity of the fluid. ReStackor calculations account for these effects using standard Reynolds number fluid dynamic relationships.
So does any of this really work?
Real world data for real pressure drops through real suspension components are available at www.supercross-online.de. Example data from supercross-online for pressure drops through the bleed circuit are shown below in comparison to ReStackor pro calculations. ReStackor matches the supercross-online orifice flow data. The 30 L/min flow rate of this bleed circuit test data is equivalent to wheel speeds of 600 in/sec in an actual suspension system. The test data spans the range of low speed to high speed suspension operation and demonstrates that ReStackor calculations are capable of accurately modeling flows through the bleed circuit over the entire range of suspension speeds. This is very important as ReStackor references shim stack changes to the effects you feel through clicker adjustments.
ReStackor orifice flow calculations accurately match dyno test data.
Viscosity Effects on Bleed Circuit Flow
The testing at supercross-online went on to evaluate effects of oil viscosity on flow rates through the orifice bleed circuits. ReStackor pro is capable of accurately computing the effects of fluid viscosity on both orifice bleed circuits as well as flow rates through the valve stack.
ReStackor calculations accurately match dyno test data measuring oil viscosity effects on bleed circuit flow rates.
