Check valve with control port to enable flow in reverse direction
Simscape / Fluids / Thermal Liquid / Valves & Orifices / Directional Control Valves
The Pilot-Operated Check Valve (TL) block models a check valve with an override mechanism to allow for backflow when activated. (A check valve in turn is an orifice with a unidirectional opening mechanism installed to prevent just that backflow.)
The override mechanism adds a third port—the pilot—to the valve. During normal operation, the pilot port is inactive and the valve behaves as any other check valve. Its orifice is then open only when the pressure gradient across it drops from inlet to outlet. Backflow, which requires the reverse pressure gradient, cannot occur. This mode protects components upstream of the valve against pressure surges, temperature spikes, and (in real systems) chemical contamination arising from points downstream.
When backflow is desired, the pilot port is pressurized and the control element of the valve—often a ball or piston—is forced off its seat. The valve is then open to flow in both directions, with a reverse pressure drop (aimed from outlet to inlet) sufficing to drive the flow upstream. (The seat, which lies in the path of the flow, determines if the valve is open. When it is covered—by a ball, piston, or other control element—the flow is cut off and the valve is closed.)
The valve opens by degrees, beginning at its cracking pressure, and continuing to the end of its pressure regulation range. The cracking pressure gives the initial resistance, due to friction or spring forces, that the valve must overcome to open by a sliver (or to crack open). Below this threshold, the valve is closed and only leakage flow can pass. Past the end of the pressure regulation range, the valve is fully open and the flow at a maximum (determined by the instantaneous pressure conditions).
The cracking pressure assumes an important role in check valves installed upside down. There, the weight of the opening element—such as a ball or piston—and the elevation head of the fluid can act to open the valve. (The elevation head can arise in a model from a pipe upstream of the inlet when it is vertical or given a slant.) A sufficient cracking pressure keeps the valve from opening inadvertently even if placed at a disadvantageous angle.
The opening of the valve depends both on the pilot pressure and on the pressure drop from inlet to outlet:
where p is gauge pressure and
k is the pilot ratio—the proportion of the pilot opening area
(SX) to the valve opening area
(SR). The subscript
X denotes a pilot value and the subscripts
B the inlet and outlet values,
respectively. The port pressures are variables determined (against absolute zero)
The pilot pressure can be a differential value relative to the inlet (port A) or a gauge value (relative to the environment). You can select an appropriate setting—Pressure differential (pX - pA) or Pressure at port X—using the Pressure control specification dropdown list. If Pressure at port X is selected:
where the subscript
Atm denotes the
atmospheric value (obtained from the Thermal Liquid Settings (TL)
or Thermal Liquid
Properties (TL) block of the model). The subscript
X,Abs denotes the absolute value at the pilot port. If
Pressure differential (pX - pA) is selected:
where the subscript
A,Abs similarly denotes
the absolute value at the inlet of the valve (port A). The
pilot pressure differential is constrained to be greater than or equal to zero—if
its calculated value should be negative, zero is assumed in the control pressure
The degree to which the control pressure exceeds the cracking pressure determines how much the valve will open. The pressure overshoot is expressed here as a fraction of the (width of the) pressure regulation range:
The control pressure (pCtl), cracking
pressure (pSet), and maximum opening
pressure (PMax) correspond to the control
pressure specification chosen (
Pressure differential or
Pressure at port A).
The fraction—technically, the overshoot normalized—is valued
0 in the fully closed valve and
1 in the
fully open valve. If the calculation should return a value outside of these bounds,
the nearest of the two is used instead. (In other words, the fraction
The normalized control pressure, p, spans three pressure
regions. Below the cracking pressure of the valve, its value is a constant zero.
Above the maximum pressure of the same, it is
1. In between,
it varies, as a linear function of the (effective) control pressure,
The transitions between the regions are sharp and their slopes discontinuous. These pose a challenge to variable-step solvers (the sort commonly used with Simscape models). To precisely capture discontinuities, referred to in some contexts as zero crossing events, the solver must reduce its time step, pausing briefly at the time of the crossing in order to recompute its Jacobian matrix (a representation of the dependencies between the state variables of the model and their time derivatives).
This solver strategy is efficient and robust when discontinuities are present. It makes the solver less prone to convergence errors—but it can considerably extend the time needed to finish the simulation run, perhaps excessively so for practical use in real-time simulation. An alternative approach, used here, is to remove the discontinuities altogether.
Normalized temperature overshoot with sharp transitions
The block removes the discontinuities by smoothing them over a specified time scale. The smoothing, which adds a slight distortion to the normalized inlet pressure, ensures that the valve eases into its limiting positions rather than snap (abruptly) into them. The smoothing is optional: you can disable it by setting its time scale to zero. The shape and scale of the smoothing, when applied, derives in part from the cubic polynomials:
In the equations:
ƛL is the smoothing expression for the transition from the maximally closed position.
ƛR is the smoothing expression for the transition from the fully open position.
Δp* is the (unitless) characteristic width of the pressure smoothing region:
f* is a smoothing
factor valued between
and obtained from the block parameter of the same name.
When the smoothing factor is
0, the normalized
inlet pressure stays in its original form—no smoothing applied—and
its transitions remain abrupt. When it is
smoothing spans the whole of the pressure regulation range (with the
normalized inlet pressure taking the shape of an
At intermediate values, the smoothing is limited to a fraction of
that range. A value of
0.5, for example, will
smooth the transitions over a quarter of the pressure regulation
range on each side (for a total smooth region of half the regulation
The smoothing adds two new regions to the normalized pressure overshoot—one for the smooth transition on the left, another for that on the right, giving a total of five regions. These are expressed in the piecewise function:
where the asterisk denotes a smoothed variable (the normalized control pressure overshoot). The figure shows the effect of smoothing on the sharpness of the transitions.
The valve is assumed to open linearly with the smoothed control pressure overshoot:
where S is sonic conductance and the
Min denote its values in
the fully open and fully closed valve. In terms of the smoothed control pressure
overshoot, the opening area becomes:
(Both expressions are used in the calculation of the pressure drop across the valve.)
The causes of those pressure losses incurred in the passages of the valve are ignored in the block. Whatever their natures—sudden area changes, flow passage contortions—only their cumulative effect is considered during simulation. This effect is captured in the block by the discharge coefficient, a measure of the mass flow rate through the valve relative to the theoretical value that it would have in an ideal valve. Expressing the momentum balance in the valve in terms of the pressure drop induced in the flow:
where ρ is density, CD is the discharge coefficient, and ξp is the pressure drop ratio—a measure of the extent to which the pressure recovery at the outlet contributes to the total pressure drop of the valve. The subscript Avg denotes an average of the values at the thermal liquid ports. The critical mass flow rate, , is calculated from the critical Reynolds number—that at which the flow in the valve is assumed to transition from laminar to turbulent:
where μ denotes dynamic viscosity. The pressure drop ratio is calculated as:
The volume of fluid inside the valve, and therefore the mass of the same, is assumed to be very small and it is, for modeling purposes, ignored. As a result, no amount of fluid can accumulate there. By the principle of conservation of mass, the mass flow rate into the valve through one port must therefore equal that out of the valve through the other port:
where is defined as the mass flow rate into the valve through port A or B.
The valve is modeled as an adiabatic component. No heat exchange can occur between the fluid and the wall that surrounds it. No work is done on or by the fluid as it traverses from inlet to outlet. With these assumptions, energy can flow by advection only, through ports A and B. By the principle of conservation of energy, the sum of the port energy flows must then always equal zero:
where ϕ is defined as the energy flow rate into the valve through one of the ports (A or B).
A— Valve entrance
Opening through which the working fluid must, during normal operation (when the pilot mechanism is disabled), enter the valve. This port can serve as an exit only when the pilot port is pressurized to a sufficient degree.
B— Valve entrance
Opening through which the working fluid must, during normal operation (when the pilot mechanism is disabled), exit the valve.
X— Pilot port
Opening by which to actuate (by the application of a sufficient pressure) the pilot mechanism that opens the valve for reverse flow.
Pressure control specification— Choice of pressure measurement to use as valve control signal
Pressure differential (pX-pA)(default) |
Pressure at port X
Choice of pressure measurement to use as pilot control signal. The block uses the chosen measurement to calculate the control pressure of the valve. (See the block description for the calculations.)
In the default setting (
Pressure differential (pX -
pA)), the control pressure is a function of the pressure
drop from the pilot port (X) to the inlet
(A). In the alternate setting (Pressure
at port X), it is a function of the gauge pressure at the
Cracking pressure differential— Effective control pressure at which the valve first opens
0.01 MPa(default) | positive scalar in units of pressure
Effective pressure differential at which the valve begins to open. This differential—the control pressure in the block description—is the sum of the pressure drop from inlet to outlet with the product of the pilot pressure and the pilot ratio. (The pilot pressure used depends on the setting of the Pressure control specification parameter.)
Maximum opening pressure differential— Effective control pressure at which the valve is fully open
0.02 MPa(default) | positive scalar in units of pressure
Effective pressure differential at which the valve is fully open. This differential—the control pressure in the block description—is the sum of the pressure drop from inlet to outlet with the product of the pilot pressure and the pilot ratio. (The pilot pressure used depends on the setting of the Pressure control specification parameter.)
Pilot ratio— Ratio of pilot port area to inlet port area
1(default) | positive unitless scalar
Ratio of the pilot port area to the inlet port area.
Maximum opening area— Opening area in the fully open position due to sealing imperfections
1e-4 m^2(default) | positive scalar in units of area
Opening area of the valve in the fully open position, when the valve is at the upper limit of the pressure regulation range.
Leakage area— Opening area in the maximally closed position due to sealing imperfections
1e-10 m^2(default) | positive scalar in units of area
Opening area of the valve in the maximally closed position, when only internal leakage between the ports remains. This parameter serves primarily to ensure that closure of the valve does not cause portions of the fluid network to become isolated (a condition known to cause problems in simulation). The exact value specified here is less important that its being a (very small) number greater than zero.
Smoothing factor— Amount of smoothing to apply to the valve opening area function
Amount of smoothing to apply to the opening area function of the valve. This parameter determines the widths of the regions to be smoothed—one located at the fully open position, the other at the fully closed position.
The smoothing superposes on each region of the opening area function a nonlinear segment (a third-order polynomial function, from which the smoothing arises). The greater the value specified here, the greater the smoothing is, and the broader the nonlinear segments become.
At the default value of
0, no smoothing is applied. The
transitions to the maximally closed and fully open positions then introduce
discontinuities (associated with zero-crossings), which tend to slow down
the rate of simulation.
Cross-sectional area at ports A and B— Area normal to the flow path at the valve ports
0.01 m^2(default) | positive scalar in units of area
Area normal to the flow path at the valve ports. The ports are assumed to be the same in size. The flow area specified here should ideally match those of the inlets of adjoining components.
Characteristic longitudinal length— Measure of the length of the flow path through the valve
0.1(default) | positive scalar in units of length
Average distance traversed by the fluid as it travels from inlet to outlet. This distance is used in the calculation of the internal thermal conduction that occurs between the two ports (as part of the smoothed upwind energy scheme employed in the thermal liquid domain).
Discharge coefficient— Empirical factor defined as the ratio of actual to ideal mass flow rates
0.7(default) | positive unitless scalar
Ratio of the actual flow rate through the valve to the theoretical value that it would have in an ideal valve. This semi-empirical parameter measures the flow allowed through the valve: the greater its value, the greater the flow rate. Refer to the valve data sheet, if available, for this parameter.
Critical Reynolds number— Reynolds number at the boundary between laminar and turbulent flow regimes
12(default) | positive unitless scalar
Reynolds number at which the flow is assumed to transition between laminar and turbulent regimes.