Installing a cable into a conduit
阅读说明:本技术 将电缆安装到管道中 (Installing a cable into a conduit ) 是由 威廉·格里福恩 亚历山大·于尔 克里斯托夫·古特伯雷 于 2019-04-03 设计创作,主要内容包括:用于将电缆安装到管道中的方法,该方法包括以下步骤:-确定最大压力,-设定泄漏塞的泄漏模式,以泄漏压降开始,泄漏压降等于或低于最大压力,-将泄漏塞附接到电缆的最前端,-将电缆的最前端引入管道中,-将加压液体供应到管道中:在供应端口处和在供应压力下,使得电缆被泄漏塞拉动,-在最前端到达第二末端之前,在靠近泄漏塞的位置处超过了泄漏压降。(A method for installing a cable into a conduit, the method comprising the steps of: -determining a maximum pressure, -setting a leakage pattern of the leakage plug, starting with a leakage pressure drop, which is equal to or lower than the maximum pressure, -attaching the leakage plug to the foremost end of the cable, -introducing the foremost end of the cable into the conduit, -supplying a pressurized liquid into the conduit: at the supply port and under supply pressure, such that the cable is pulled by the leakage plug, -the leakage pressure drop is exceeded at a location close to the leakage plug before the foremost end reaches the second end.)
1. Method for installing a cable (1) into a conduit (3) having two ends, the method comprising the steps of:
-determining a maximum pressure (p) based on the burst pressure or working pressure of the pipe (3) taking into account the installation temperature and/or the installation timemax),
-setting the leakage pattern of the leakage plug (7) to a leakage pressure drop (Δ ρ) over the entire leakage plug (7)Leakage of) Initially, the leakage pressure drop is determined to be equal to or lower than the maximum pressure (p)max),
-attaching the leakage plug (7) to the foremost end of the cable (1),
-introducing the forwardmost end of the cable (1) into the conduit (3) at a first end (31),
-supplying a pressurized liquid into the conduit (3):
supplying a pressurized liquid into the conduit at a supply port arranged between the foremost end equipped with the leakage plug (7) and the first end (31), and
at the supply pressure (p)sup) Supplying pressurized liquid into the conduit at a supply pressure equal to or higher than a predetermined pressure,
so that the cable (1) is pulled by the leakage plug (7),
-the leakage pressure drop (Δ ρ) is exceeded at a position close to the leakage plug (7) before the foremost end reaches a second end (32)Leakage of) Causing the leakage mode to begin.
2. Method according to the preceding claim, wherein the duct (3) presents a trajectory with a non-constant height, comprising the steps of: adjusting the supply pressure (p) before the foremost end reaches the second end (32)sup) Such that along the portion of the duct (3) between the first end (31) and the foremost end of the cable (1) filled with liquid, the pressure of the liquid is each lower than the maximum pressure (p)max)。
3. The method according to the preceding claim, wherein the supply pressure is regulated so that, at any point along the portion of the duct (3) between the first end (31) and the forwardmost end of the cable (1) filled with liquid:
-for a point at a height above said first end (31), said supply pressure (p)sup) Less the pressure loss caused by the viscosity of the liquid reaching the point considered, greater than the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the point considered and the height of the first end (31), and/or
-said supply pressure (p) for a point at a lower level than said first end (31)sup) Less the pressure loss caused by the viscosity of the liquid reaching the point considered, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the point considered and the height of the first end (31), is greater than zero and lower than the maximum pressure (p)max)。
4. The method of any of claims 1-3, wherein:
-adjusting the supply pressure (p) if the second end is located at a higher level than the first endsup) Such that said supply pressure (p)sup) Minus the pressure loss caused by the viscosity of the liquid over the entire length of the pipe, minus the leakage pressure drop (Δ p)Leakage of) Equal to the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the second end and the height of the first end, or
-adjusting the supply pressure (p) if the second end is located at a lower height than the first endsup) Such that said supply pressure (p)sup) Minus the pressure loss caused by the viscosity of the liquid over the entire length of the pipe, minus the leakage pressure drop (Δ p)Leakage of) And, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the second end and the height of the first end, is equal to 0.
5. The method according to any one of the preceding claims, further comprising the step of: when the leakage mode is started, the pressurized liquid is supplied at a flow rate exceeding the leakage flow rate of the leakage plug (7).
6. Method according to any of the preceding claims, wherein before the start of the leakage mode, a flow rate Φ defined in the following formula is usedvSupplying the pressurized liquid:
wherein:
Φvis the flow rate (m) of the supplied pressurized liquid3/s),
DcIs the outer diameter (m) of the cable (1),
Ddis the inner diameter (m) of the pipe (3),
vcable with a protective layerIs the speed (m/s) at which the cable (1) enters the conduit.
7. The method of any preceding claim, wherein:
-the two ends are located at different heights, and
-introducing the forwardmost end of the cable (1) at the first end (31) of the duct (3), which is the end located at the highest height.
8. Method according to any of the preceding claims, wherein the leakage pressure drop (Δ ρ) is adjusted during installationLeakage of) And wherein:
-said leakage pressure drop (Δ p)Leakage of) Increase before the leakage plug (7) travels through the uphill section of the pipe (3), or gradually during the travel of the leakage plug through the uphill section of the pipe, or
-said leakage pressure drop (Δ p)Leakage of) -reducing before or during the travel of the leakage plug (7) through the downhill section of the pipe (3).
9. The method according to any of the preceding claims, wherein the method comprises the following initial steps:
-measuring or determining the inner diameter of the pipe (3), the outer diameter of the cable (1) and the slope of the pipe (3) between its ends,
-setting the leakage surface of the leakage plug (7) equal to or greater than the diameter DHole(s)The surface of the circular hole of (a):
more preferably:
even more preferably:
wherein:
wherein:
Dcis the outer diameter (m) of the cable (1),
Ddis the inner diameter (m) of the pipe,
Δpleakage ofIs the leakage pressure drop (Pa) across the leakage plug (7),
ρwis the density (kg/m) of the pressurized liquid3),
Alpha is the average angle of the pipe (3) to the horizontal plane,
g is the acceleration of gravity (9.81 m/s)2),
μwIs the dynamic viscosity (Pas) of the pressurised liquid.
10. Method according to claim 1, wherein the pipe (3) has an almost horizontal trajectory, and wherein the method comprises the initial steps of:
-measuring or determining the inner diameter of the pipe (3), the outer diameter of the cable (1),
-setting the leakage surface of the leakage plug (7) equal to or greater than the diameter DHole(s)The surface of the circular hole of (a):
more preferably:
even more preferably:
wherein:
wherein:
Dcis the outer diameter (m) of the cable (1),
Ddis the inner diameter (m) of the pipe,
Δpleakage ofIs the leakage pressure drop (Pa) across the leakage plug (7),
ρwis the density (kg/m) of the pressurized liquid3),
μwIs the dynamic viscosity (Pas) of the pressurised liquid.
11. Method according to any one of the preceding claims, wherein the flow rate of the pressurized liquid supplied into the conduit (3) is:
-before the leakage mode starts, is set to a first flow value Φv1,
-after the start of the leakage mode, set to a second flow Φv2,
Wherein phiv2≥5Φv1。
12. The method according to any one of the preceding claims, comprising the steps of: before the leak mode begins, the pump used to supply the pressurized liquid is changed.
13. The method according to any one of the preceding claims, the method comprising:
-a step of measuring the pressure during installation at a location close to the leakage plug (7),
-correcting the supply pressure (p) according to the pressure measured at a position close to the leakage plug (7)sup) The step (2).
Technical Field
The present invention relates to the installation or introduction or laying of cables into pipelines.
Background
Installation of the cable into a pipeline (buried or located on the seabed) may be achieved by floating techniques. In this technique, a cable is introduced into a conduit and a pressurized liquid is introduced simultaneously to generate a drag force along the cable to push the cable into the conduit. However, this technique for introducing large power cables into very large pipes requires very high flow rates, resulting in a high volume of liquid being supplied at the inlet of the pipe and discharged at the outlet of the pipe. In addition, high-flow pumps are required.
Installation of the cable into the pipeline (buried or located on the seabed) may also be achieved by pulling pigs (pull pigs) attached along the cable to push the cable by the pulling force generated by the pressurized liquid, but in this case too much pressure may damage the pipeline (risk of bursting) or the cable (risk of rupture). As disclosed in document WO2011054551a2, a liquid may be used when the pulling pig is attached to the cable.
Disclosure of Invention
The present invention aims to solve the above-mentioned drawbacks of the prior art and firstly proposes a method for installing a cable into a conduit, which method reduces the risk of damaging the conduit or the cable and/or reduces the risk of the need for liquid supply, while still aiming to run the cable through a long conduit.
To this end, a first aspect of the invention is a method for installing a cable into a conduit having two ends, the method comprising the steps of:
-determining a maximum pressure based on a burst pressure or working pressure of the conduit and/or based on a maximum strength of the cable,
-setting the leakage pattern of the leakage plug to start with a leakage pressure drop over the leakage plug, which is determined to be equal to or lower than the maximum pressure,
-attaching a leakage plug to the foremost end of the cable,
-introducing the foremost end of the cable into the conduit at the first end,
-supplying a pressurized liquid into the conduit:
supplying a pressurized liquid into the conduit at a supply port arranged between a forwardmost end provided with a leakage plug and the first end, and
supplying a pressurized liquid into the conduit at a supply pressure, the supply pressure being equal to or higher than a predetermined pressure,
so that the cable is pulled by the leakage plug,
-the leakage pressure drop is exceeded at a position close to the leakage plug before the foremost end reaches the second end, resulting in the leakage pattern starting. In other words, the above method proposes to use a pulling technique (no or almost no leakage at the leakage plug) in the first stage and a technique similar to the floating technique (large leakage of liquid at the leakage plug) to lay the cable into the pipeline in the second stage. During the first phase, the liquid supply is limited to the flow required to "follow" the cable (so no significant additional flow is required), and during the second phase, the pressure at the side of the leakage plug is no greater than the maximum pressure (so no excessive pressure is applied to the pipe wall or the cable).
According to one embodiment, the conduit exhibits a trajectory having a non-constant height, and the method comprises the steps of: the supply pressure is regulated before the forwardmost end reaches the second end, so that along the portion of the conduit between the first end and the forwardmost end of the cable filled with liquid, the pressure of the liquid is lower than the maximum pressure. In other words, the predetermined supply pressure is adjusted according to the slopes along the pipe and the distance of these slopes from the liquid inlet.
Advantageously, the maximum pressure is also determined taking into account the installation temperature and/or the installation time. In other words, as the first parameter considered, the value of the burst pressure or working pressure depends on the operating temperature and/or the installation time.
Advantageously, the supply pressure is regulated so that, at any point along the portion of the duct between the first end and the forwardmost end of the cable filled with liquid:
-for a point at a height above the first end, the supply pressure minus the pressure loss caused by the viscosity of the liquid reaching said considered point is greater than the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of said considered point and the height of the first end, and/or
-for points at a height lower than the first end, the supply pressure minus the pressure loss caused by the viscosity of the liquid reaching said considered point, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of said considered point and the height of the first end, is greater than zero and lower than the maximum pressure.
Advantageously, the method further comprises the steps of: when the leak mode is initiated, pressurized liquid is supplied at a rate that exceeds the leak rate of the leak plug. During the second phase, the leakage plug is significantly opened in order to allow a substantial increase in the flow to be supplied at the supply port in order to push the cable with a significant drag force along the entire cable length.
Advantageously, before the start of the leakage mode, the flow Φ defined in the formula isvSupplying a pressurized liquid:
wherein:
Φvis the supplied pressurized liquid flow rate (m)3/s),
DcIs the outer diameter (m) of the cable,
Ddis the inner diameter (m) of the pipe,
vcable with a protective layerIs the velocity (m/s) of the cable into the conduit.
According to the above embodiment, during the first phase (before the start of the leakage mode) no or hardly any substantial liquid flow passes the closed or almost closed leakage plug.
Advantageously:
the two ends are located at different heights, and
-introducing the forwardmost end of the cable at a first end of the conduit, the first end being the end located at the highest level. The forwardmost end of the cable is introduced at the first end of the duct so that, due to the liquid density and the height difference between the highest level of the first end and the height of the forwardmost end, the pressure exerted at a location close to the leakage plug gradually increases while the leakage plug moves towards the second end located at the lowest level. The method is particularly suitable for laying cables in pipes which are oriented (usually) downhill. In other words, the installation is preferably done with the highest end to push the cable to the lowest end, since the leakage mode will automatically start when the supply pressure plus hydrostatic pressure exceeds the leakage pressure drop, thereby protecting the pipe and/or cable from excessive pressure. This method with medium term opening allows the installation of cables using a strict pulling technique (low demand for liquid) until the height difference switches the switch to leakage mode to avoid overpressure duct damage.
In summary, one aspect of the invention relates to a method for installing a cable into a conduit having two ends located at different heights, the method comprising the steps of:
-determining a maximum pressure based on a burst pressure of the conduit and/or based on a maximum strength of the cable,
-setting the leakage pattern of the leakage plug to start with a leakage pressure drop over the leakage plug, which is determined to be equal to or lower than the maximum pressure,
-attaching a leakage plug to the foremost end of the cable,
-introducing the forwardmost end of the cable into the conduit at the end having the highest height,
-supplying a pressurized liquid into the conduit:
supplying pressurized liquid into the conduit at a supply port arranged between a forwardmost end provided with a leakage plug and an end having the highest height, and
supplying a pressurized liquid into the conduit at a supply pressure, which is equal to or higher than a predetermined pressure,
so that the cable is pulled by the leakage plug,
-the leakage pressure drop is exceeded at a position close to the leakage plug before the foremost end reaches the lowest level end, resulting in the leakage pattern starting.
Advantageously, the supply pressure is set such that:
-the supply pressure minus the pressure loss caused by the viscosity of the liquid reaching the foremost end of the cable, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the end of highest height and the height of the foremost end of the cable,
is less than:
-a maximum pressure. According to this embodiment, the supply pressure is calculated and limited to avoid any excessive stress along the downhill pipeline.
Advantageously, the supply pressure is set such that:
-the supply pressure minus the pressure loss caused by the viscosity of the liquid reaching the second end, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the two ends,
is less than:
-a maximum pressure. According to this embodiment, the supply pressure is calculated and limited to avoid any excessive stress along the downhill pipeline.
Advantageously, the supply pressure is set such that:
-the supply pressure minus the pressure loss caused by the viscosity of the liquid reaching a portion of the pipe having a height lower than the height of the second end, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the first end and the height of the portion of the pipe having a height lower than the height of the second end,
is less than:
-a maximum pressure. According to this embodiment the supply pressure is calculated and limited such that any excessive stress along the downhill pipeline is avoided even if a part of the pipeline is located below the second end (at a lower level).
In any case, the predetermined pressure is equal to or higher than the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the first end and the height of the portion of the conduit having a height higher than the height of the first end. According to this embodiment the supply pressure is calculated such that it is ensured that the pipe will be filled with liquid even if a part of the pipe is located above the first end (at a higher level).
Advantageously, during installation, the leakage pressure drop is regulated, and:
-the leakage pressure drop increases before the leakage plug travels through the uphill section of the pipe, or gradually during the travel of the leakage plug through the uphill section of the pipe, or
-the leakage pressure drop is reduced before or gradually during the travel of the leakage plug through the downhill section of the pipe. According to this embodiment, the leakage plug is (remotely) controlled during installation to adjust its leakage pressure drop according to the rise/fall conditions. Particularly advantageously, the leakage pressure drop is performed after the leakage plug reaches a portion of the duct located at a level lower than the second end, and travels upwards with an increase in its height; this avoids the pipe being subjected to excessive stress at its lowest level.
Advantageously:
-adjusting the supply pressure (p) if the second end is located at a higher level than the first endsup) So that the supply pressure (p) issup) Minus the pressure loss caused by the viscosity of the liquid over the entire length of the pipe, minus the leakage pressure drop (Δ p)Leakage of) Equal to the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the second end and the height of the first end, or
-adjusting the supply pressure (p) if the second end is located at a lower height than the first endsup) So that the supply pressure (p) issup) Minus the pressure loss caused by the viscosity of the liquid over the entire length of the pipe, minus the leakage pressure drop (Δ p)Leakage of) And, plus the hydrostatic pressure caused by the density of the liquid and the difference in height between the height of the second end and the height of the first end, is equal to 0.
The above-described embodiment of adjusting the supply pressure according to the above-described conditions ensures that the pipe is filled with water even if the trajectory is not at a constant height and even if the leakage plug is in leakage mode.
Advantageously, the method comprises the following initial steps:
-measuring or determining the inner diameter of the pipe, the outer diameter of the cable and the slope between the ends of the pipe,
-setting the leakage surface of the leakage plug equal to or larger than the surface of the circular hole having a diameter:
wherein:
wherein:
Dcis the outer diameter (m) of the cable
DdIs the inner diameter (m) of the pipe
ΔpLeakage ofIs the leakage pressure drop (Pa) across the entire leakage plug
ρwIs the density (kg/m) of the pressurized liquid3)
Alpha is the average angle of the pipe to the horizontal
g is the acceleration of gravity (9.81 m/s)2)
μwIs the dynamic viscosity (Pas) of the pressurized liquid.
According to the above embodiment, once the leakage pattern begins, the leakage surface is calculated to allow a large amount of liquid flow.
Advantageously:
advantageously, the flow rate of the pressurized liquid supplied into the duct is:
before the start of the leakage mode,is set to a first flow value phiv1,
-after the start of the leakage mode, set to a second flow Φv2,
Wherein phiv2≥5Φv1。
In other words, one aspect of the present disclosure relates to the use of a leakage plug or a leakage plug having a leakage surface equal to the surface of a circular hole having a diameter that meets the following criteria:
if the pipe has a horizontal or nearly horizontal trajectory (the slope of the pipe from the horizontal is equal to or not greater than 5 °), the method comprises the initial steps of:
-measuring or determining the inner diameter of the pipe, the outer diameter of the cable,
-setting the leakage surface of the leakage plug equal to or greater than the diameter DHole(s)The surface of the circular hole of (a):
more preferably:
wherein:
wherein:
Dcis the outer diameter (m) of the cable,
Ddis the inner diameter (m) of the pipe,
Δpleakage ofIs the leakage pressure drop (Pa) across the entire leakage plug,
ρwis the density (kg/m) of the pressurized liquid3),
μwIs the dynamic viscosity (Pas) of the pressurized liquid.
Advantageously:
wherein:
wherein:
Dcis the outer diameter (m) of the cable,
Ddis the inner diameter (m) of the pipe,
Δpleakage ofIs the leakage pressure drop (Pa) across the entire leakage plug,
ρwis the density (kg/m) of the pressurized liquid3),
μwIs the dynamic viscosity (Pas) of the pressurized liquid.
Advantageously, the method comprises the steps of: before the leak mode begins, the pump used to supply the pressurized liquid is changed.
Advantageously, the method comprises:
-a step of measuring the pressure during installation at a location close to the leakage plug,
-a step of correcting the supply pressure on the basis of the pressure measured at a position close to the leaky plug.
Drawings
Other features and advantages of the invention will appear more clearly from the following detailed description of a particular non-limiting example of the invention, illustrated by the accompanying drawings, in which:
figure 1 shows an overall view of the installation of a cable into a duct using the method according to the invention;
figure 2 shows an example of a pulling pig that can be used during the installation shown in figure 1;
figure 3 shows an example of a trajectory of the pipe of figure 1, in which the pressure inside the pipe varies along its length;
figure 4 shows a pressure profile for installing a cable into the pipe of figure 3 according to a first scenario;
fig. 5 shows a liquid flow through a pulling pig during installation of the cable in the duct of fig. 3 according to a first scenario;
fig. 6 shows a pressure profile for installing a cable into the pipe of fig. 3 according to a second scenario;
fig. 7 shows a pressure profile for installing a cable into the pipe of fig. 3 according to a third scenario;
fig. 8 shows a pressure profile for installing a cable into the pipe of fig. 3 according to a fourth scenario;
fig. 9 shows a pressure profile for installing a cable into the pipe of fig. 3 according to a fifth scenario;
fig. 10 shows a pressure profile for installing a cable into the pipe of fig. 3 according to a sixth scenario.
Detailed Description
Fig. 1 shows an overall schematic view of the installation of a
In order to push the
Fig. 2 shows a detailed view of a preferred embodiment of the
Optionally, a force sensor (not shown) may also be installed between the
The cylindrical valve 13 may completely block the opening 14 so that the
In the leakage mode, a pressure drop will occur depending on the size of the holes and openings through which the liquid passes. This pressure drop will be referred to as leakage pressure drop Δ p in the followingLeakage of。
According to another embodiment, not shown, the
According to a further embodiment, the spring may be pushed by a (pulling) force between the cable and the leakage plug, thereby with a preset force (or pressure drop Δ p)Leakage of) And (4) opening.
A first aspect of the present disclosure relates to the use of a
After a considerable distance or after a number of turns or bends, the pressure is compensated by friction or by traction effects, so that the maximum distance that can be achieved in the first (non-leaking) mode is achieved.
A first aspect of the present disclosure providesA switch from a first mode to a second mode corresponding to a floating technique is presented. For this reason, if a predetermined pressure (hereinafter referred to as "leakage pressure drop" or Δ p) is appliedLeakage of) The
Thus, the mounting method comprises the steps of: the liquid pressure is increased to force the
In other words, during the first phase, the liquid flow is limited to a minimum to follow only the leaky plug (in non-leaky mode, so that there is no significant speed difference between the liquid and the cable 1), and once the maximum distance is reached in this non-leaky mode, the pressure is increased to force the
In detail, during the first phase, the liquid flow Φ is defined by the following equationv:
Wherein:
Φvis the supplied pressurized liquid flow rate (m)3/s),
DcIs the outer diameter (m) of the cable,
Ddis the inner diameter (m) of the pipe,
vcable with a protective layerIs the velocity (m/s) of the cable into the conduit.
If the
During the second phase, the liquid flow is multiplied by a factor of at least 2, preferably 5, to generate a sufficient drag force. Advantageously, the method may comprise the step of changing the pump supplying the liquid (or adding a second pump): during the first phase, the first pump has a "low" flow rate and a "medium or high" pressure capacity, and during the second phase, the second pump has a "high" flow rate and no reduced pressure capacity.
The
A second aspect of the present disclosure is the use of a
In this case, the invention proposes a specific strategy for laying the
In particular, in the case of a trajectory as shown in fig. 3, the
Then, the
Hereinafter, the horizontal pressure phorIs defined as the pressure present in the
For a
along a conduit section with a cable
Along the pipe section without cable (behind the leakage plug 7)
Here, x is a coordinate describing a position in the pipe, 0 at the supply port (first end 31) and x at the end of the pipe (second end 32)End part。ΔpviscIs the total viscous pressure drop caused by the flowing liquid:
here,. phi.,. phi.VIs the volume flow rate, DdIs the diameter of the pipe, DcIs the diameter of the cable, muwIs the dynamic viscosity of a liquid(water 0.0011Pas), pwIs the density of the liquid (1000 kg/m water)3) And D ishydroIs the hydraulic diameter.
In the case of a trajectory incline (i.e. a pipe trajectory following a varying height), the hydrostatic pressure p must be taken into accounthydrBecause of the effective pressure p to which the
This can be done by applying a hydrostatic pressure phydrAdded to horizontal pressure phorTo complete. Hydrostatic pressure p relative to the supply porthydrIs equal to
phydr=-ρwg(zx-zsup),
Wherein z isxAnd zsupIs the height (positive up) at position x and the supply port, respectively. It is easier to define the hydrostatic height function ρ graphicallywg(zx-zsup) Then needs to be driven from the horizontal pressure phorSubtracting the hydrostatic height function to obtain an effective pipe pressure p along the section of pipe having the cableeff:
peff(x)=phor(x)-ρwg(zx-zsup)
According to a first scenario, fig. 4 shows the hydrostatic height function ρ when installing the
Note that: while the
Note also that from the latter case, the boundary condition Δ p may be calculatedvisc(and the flow rates derived therefrom):
Δpvisc=psup-ρwg(z2-zsup)-Δpleakage of
According to the invention, the supply pressure psupAnd the leakage pressure deltap over the
peff(x) Not less than 0 or phor(x)≥ρwg(zx-zsup) (1)
At position xLow 3In the lowest point (right-hand depression in the height distribution) of (a), the maximum pressure p is indicatedmax. This pressure must not be higher than the maximum pressure that the
peff(x)≤pmaxor phor(x)-ρwg(zx-zsup)≤pmax(2)
Note that when the recess is at "depth" hDepressions(on both sides) to result in ρwghDepressionsGreater than the maximum pressure pmaxThen, equation (2) cannot be satisfied.
Also note that the supply pressure p at the inletsupIs chosen just enough to make the horizontal pressure phorAt position x2Is related to hydrostatic pressure phydrTangent or just at hydrostatic pressure phydrTo ensure that the loss of viscosity does not prevent the
FIG. 5 shows the flow through the
The different positions of the
Then, when point a is reached, the
Then, when the depression in the
Then, the
According to a second scenario, fig. 6 shows the hydrostatic height function ρ when installing the
According to a third scenario, fig. 7 shows the hydrostatic height function ρ when installing the
Note that the supply pressure p can also be setsupAnd the leakage pressure deltap across the leakage plugLeakage ofSo that the viscous pressure drop Δ pviscMinimized (i.e., less traffic).
According to a fourth scenario, fig. 8 shows the hydrostatic height function ρ when installing the
In fig. 9, the
However, once the effective pressure equals the maximum pressure pmaxThe
It will, of course, be understood that obvious improvements and/or modifications may be effected by those skilled in the art, while remaining within the scope of the invention as defined by the appended claims.
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