Waves from ships

What they say and what the waves from the ships are silent about.

The formation of a wave from moving ships has much more hidden meaning than it might seem at first glance.

So the bow wave arises from the pushing apart of the masses of water by the hull of the ship invading them.

At the same time, it is logical to assume that the magnitude of the created wave per unit time in terms of volume should correspond to the volume of the ship’s hull that invaded during the same time.

It follows from this that the bow wave is formed in a given section of space all the time while the ship pushes the water apart in it.

But what happens to a wave when a section of a ship with straight sides and a bottom begins to move along a given section, then there are no more volume changes in this section?

At the moment of transition from the curved nose to the rectilinear section of the hull, the wave ceases to be generated, and the previously created wave breaks away from the side and goes into space, taking with it both the volume of water displaced by the nose and the energy spent on wave generation.

At the end of the straight section of the hull, there is inevitably a stern, on which the narrowing of the hull section begins.

In the place of the narrowing of the hull, water begins to fill the empty volume following the retreating board.

That is, a reverse wave occurs.

At the same time, the water flowing towards the side moves in the direction of lowering the level, since gravity at the difference in the heights of the water levels is the only driving force for the horizontal movement of calm water towards the retreating side.

It turns out that there is also a stern wave, but it looks like a smooth depression near the side.

In the photo of moving ships, the bow wave is visible in all its glory from different angles, but it is almost impossible to see the stern wave.

On rare frames, where it is possible to see a certain divergent wave behind the ship, it subsequently turns out that these are not “stern”, but “AFTER waves”, created when converging imperceptible stern waves cross and move to the sides opposite the ship.

Mutual compensation of bow and stern waves at the meeting.

A striking phenomenon of the close meeting of the bow and stern waves is the movement of gentle gliding boats.

In planing boats, the bow wave directly passes into the stern wave, since the boat does not have a long section of the straight side.

At the same time, the bow expanding towards the stern is abruptly cut off by a vertical cut of the stern without any smooth transitions.

Thus, behind the stern of the glider there is a visually observed deep water hole, which begins to fill with water immediately after the boat leaves it.

It is these shafts of water that join in the “water hole” from two sides, when they meet, generate a powerful splash of water behind the stern of the boat, and from the same splash the after waves begin to scatter to the sides.

Since the bow wave does not have time to break away from the boat due to the lack of a straight section of the side, the hump of the bow wave collapses back into the “water hole” behind the stern of the glider. As a result, the bow wave loses its potential not far from the wake of the boat, while divergent shafts of the bow wave at an angle of 20 degrees to the course are not formed at all (see Fig. 2-3)

Fig.1. Bow waves are clearly visible, diverging from the bows of the ships. You can also see an inconspicuous strip of the after wave behind the first ship.

Fig.2. Bow waves are clearly visible, diverging from the nose of a giant container ship. You can also see behind the stern an inconspicuous strip of the after wave, while in the zone of narrowing of the stern within the ship near the stern from below (where there are no disturbances from the green boat) there is no disturbance of the back wave at all.

Fig.3. The wake of a high-speed gliding boat. There are no bow waves emanating from the bow of the boat. In the wake stream, only two parallel foam strips from the bow breakers of the port and starboard sides are visible.

Fig.4. Rows of bow and stern waves separated by space are clearly visible. It can be seen that the astern waves occur in the foam surf from the propeller behind the edge of the stern.

Fig.5. Rows of bow and stern waves separated by space are clearly visible. It can be seen that the astern waves occur in the foam surf from the propeller behind the edge of the stern. Intersecting rows of waves from the noses of different ships practically do not mix and continue their diverging path even after crossing each other.

Fig.6. Rows of bow and stern waves separated by space are clearly visible.

Fig.7. Rows of bow and stern waves separated by space are clearly visible. It can be seen that the astern waves occur in the foam surf from the propeller behind the edge of the stern. Of particular interest is the sinus-shaped expanding foam trail from the screws, that is, the exit to the surface of the water bundles twisted by the screws has an unstable-cyclic oscillatory character.

Fig.8. A view of the collapse of the bow wave from the planing boat into the “water hole” astern, after which the bow wave no longer propagates sideways from the ship. Also visible is the “cock of waves” from the helical jet and the impact meeting of the closing walls of the “water pit”, from which rapidly damping after waves depart to the sides.

Fig.9. The movement of a short boat in a displacement mode. The nasal wave is not strongly expressed. But you can see the collapse of the bow wave from the boat into the “water hole” behind the stern, after which the bow wave no longer spreads sideways from the ship. Also visible is the “cock of waves” from the helical jet and the shock meeting of the closing walls of the “water pit”, from which sharply expressed after-stern waves depart to the sides.

Fig.10. Visual comparison of waves from a displacement large ship and a planing short boat. The bow wave is strongly pronounced in a large displacement vessel. But to the glider you can clearly see the collapse of the bow wave from the boat into the “water hole” behind the stern, after which the bow wave no longer spreads sideways from the ship. For both vessels, a “rooster of waves” is visible from the helical jet and the shock meeting of the closing walls of the “water pit”, from which sharply pronounced after waves depart to the sides.

Fig.11. Supertanker at full speed, view from the stern. It is not possible to see the feeding pit on the narrowing of the stern. A foamy breaker is also visible near a deeply submerged propeller.

Fig.12. View of the stern of an unloaded supertanker in the port. The smooth narrowing of the straight hull towards the stern is clearly visible.

Fig.13. Supertanker without cargo at full speed from the stern. It is not possible to see the feeding pit on the narrowing of the stern, but the foamy breaker from the work of the semi-submerged propeller is perfectly visible.

Fig.14. Single propeller of an Aframax vessel. Belonging to Aframax is determined by the scale on the tail rotor, where the 12m mark is much lower than the waterline at the border of the rudder blade, that is, the total draft is more than 15m. The same scale shows that the diameter of the screw is about 9 m, while the axis of the screw is at a height of 5 m from the level of the bottom of the vessel and does not reach the bottom of the shallow channel by about 0.5 m at extremely small gaps between the bottom and the bottom.

Evaluation of propeller traction characteristics based on the power of the tanker’s power plant.

Since we know the size of the Aframax tanker and the power of its power plant, we can use them to evaluate the tag characteristics of the propeller. It is also possible to estimate the acceleration of the water flow by the propeller to obtain the calculated thrust of the propeller.

To begin with, you can evaluate the traction of wine, since the power of the power plant is known = 15 thousand kW and the speed is 14 knots (7 m / s).

When calculating the propeller thrust from the engine power, it is necessary to take into account the propeller efficiency, which for a supertanker in the nominal and most economical mode of motion can be considered close to a maximum of 70% (see Fig. 15.)

Fig.15. Graphs of efficiency values of various propellers on the speed of the vehicle.

Then the propeller thrust with an efficiency of about 0.7 or 70% will be:

F=15*10^6*0.7/7=1.5 thousand kN or 150 tons.

With a propeller diameter of about 9 m (see Fig. 14), the area of the propeller circle will be:

Sv \u003d 9 ^ 2 * 3.14 / 4 \u003d 63.6 m2

If we consider the propeller to be completely covering its circle with blades (see Fig. 14), then the average pressure on the propeller from useful thrust in the plane of the propeller will be Рв=150/63.6=2.36 tons/m2 or 23.6 kPa.

That is, it is less than the frontal velocity head pressure of 24.5 kPa on the stem at a travel speed of 7 m/s.

Knowing the cross-sectional area of the submerged part of the hull of about 630 m2 and the propeller thrust of 150 tons, we find that the average pressure of the hull resistance is almost 10 times less than the velocity head at a given ship speed.

From which it follows that the experimentally confirmed Cd for the tanker is only Cd = 0.1. (see tab. Fig. 17-last line). That is, the streamlining of huge ships at high Reynolds numbers really drops sharply in comparison with the flow around small bodies in laboratory measurements (see Fig. 16)

Fig.16. Table of Cd values for various bodies of revolution (left table) and long rods of various profiles (right table). Cd is the coefficient of dynamic head resistance in relation to the cross-sectional area of the test body. You can clearly see that the values in the left table are smaller than those on the right. That is, the flow around single bodies from all four sides is much more profitable than the flow around from two sides for linearly extended objects.

Do not confuse Cd and Cx. Since in Cx the resistance is attributed to the largest cross-sectional area of the entire body (usually the wing area of an aircraft), while for Cx the area of this section is not perpendicular to the direction of motion of the medium around the body, which leads to the appearance of absurdly low Cx for resistances in strongly elongated teardrop-shaped bodies and thin flat wings.

Fig.17 Table of Cx coefficients for bodies of revolution. According to the previously given calculations, the hydraulic resistance of an Aframax tanker with a blunt bulb and vessel size in terms of 42x245m just falls into the category of drop-shaped bodies with an elongation L / D = 6 (the last lower part of the table).

Propeller water acceleration

To obtain the calculated thrust, the ship’s propeller must discard a certain amount of water with an increment of additional speed, which follows from the law

F=m*a=d(m*V)

A thrust of 150 tons for a water screw means an increase in momentum due to an increase in jet speed

F=m*dV

In this case, m \u003d Sv * q * Vc,

Where q= 1000kg/m3 is the density of water and the speed of the ship is Vc=7m/s

Where

dV=F/(S*q*V)=1.5*10^6/(63.6*1000*7)=3.37m/s

In this case, the speed of the ends of the blades is approximately 44 m / s, if we assume that in one revolution of the propeller the vessel travels a distance equal to the diameter (optimal pitch of the propeller).

In this case, the slope of the helix will be 1/(2*3.14)=0.16

With a constant volume of incompressible water, the acceleration of the flow by 2.4 m/s from 7 to 10.4 m/s means a decrease in the cross-sectional area of the water jet from Sv=64m2 to Sst=Sv*Vc/Vct

Sst \u003d 64 * 7 / 10.4 \u003d 43.1 m2

In this case, the diameter of the jet after the propeller will be

Dst \u003d Dv * (Sst / Sv) ^ 0.5 \u003d 9 * (43.1 / 64) ^ 0.5 \u003d 9 * 0.82 \u003d 7.39m

That is, due to the acceleration of the jet after the screw and its narrowing, an additional dip in the water immediately after the screw occurs by the value of this narrowing of the jet.

After a shock collision with the surrounding masses of water, the jet from the propeller slows down and bends upwards towards the surface, since it is easier for it to move towards the surface than through the thickness of incompressible water. This is how the exit of the “rooster” of the foamy breaker from the helical jet that has surfaced to the surface occurs.

As a result of intensive rotation, a strong rarefaction occurs in the center of the water vortex, which leads to the formation of a stable funnel with atmospheric air suction when the jet ascends from the propeller to the surface (see Fig. 18)

So for the propeller of the ship Afromax D=9 m and rotational speed n=1.5 rpm (w= 9rad/s), and the rarefaction in the vortex on the propeller axis will reach the value:

Р= a*q*h=(w^2*R)*q*R=9^2*1000*(9/2)^2=1.6 MPa (or Р=16atm=160m.water.st) .

That is, a breakthrough of air to the propellers of displacement ships is almost inevitable, since the rarefaction in the vortex is much greater than the compressing static pressure from the water column to the surface.

This is the reason for the intense white foaming of water from under the propellers, even in large vessels with deeply flooded propellers.

Fig.18. Picture from a textbook demonstrating an air funnel to the water surface from the rarefaction in the center of a rapidly rotating water vortex from a propeller. Together with the funnel, it follows to the surface of the water and the entire water vortex from the propeller.

What is the efficiency of the propeller

Useful work of 70% of the screw is spent on pushing the ship through the water to overcome its resistance.

Then what is the remaining 30% of power loss minus 70% efficiency spent on?

So you can use the rest of the energy to accelerate the water thrown by the propeller in different directions.

The proportion of efficiency losses due to axial and rotational acceleration of water by the propeller

The increment of the longitudinal kinetic energy in the propeller jet from the increase in speed dV=3.37m/s will be:

Ext \u003d Sv * Vs * q * (dV) ^ 2 / 2 \u003d 64 * 7 * 1000 * (3.37) ^ 2 / 2 \u003d 2544 kJ

That is, taking into account the estimated power of 15 thousand kW on the shaft of the power plant, the loss in dynamic pressure will be

2544/15000=0.167 or 16.7% power.

If we consider a propeller with an efficiency of about 70%, then out of 30% losses, 16.7% goes into the additional axial velocity of the jet from the propeller, and the remaining 13.3% should go into the rotational component of the jet. The division of propeller losses by axial and rotational components is shown in the conditional graph (see Fig. 19)

In our calculation, we evenly divide the component from the profile resistance of the blades between the axial and radial increases in flow speeds, without separating it into a separate calculated value.

Fig.19. Distribution of useful power and propeller losses into components of axial speed and propeller rotation. On the X axis, the values of the conditional screw pitch Lr \u003d V / (n * D), where n is the rotational speed of the screw (revolution / s), which for the step L \u003d D corresponds to Lr \u003d 0.5

Since we know the energy and diameter of the jet, the average circumferential velocity of the swirling jet flow after the screw should give us a value of 13% of the total jet energy, while we consider the energy at the average flow velocity at Rcr = 0.68 * Rv of the screw radius.

Where Rcp=0.68 is the result from the calculation below.

0.13*Ndv= Sv*Vc*q* (Vlop*Rav)^2/2

0.13=64*7*1000*(44*0.68)^2/(2*15000000)

That is, in the end, according to the calculation, it turns out that the operation of the propellers does not increase the flow of water when flowing around the hull, but creates an intense surf already astern from the swirling and accelerated flow from the propeller. In this case, the flow acceleration is very insignificant in magnitude.

Comparison of the theoretical and experimental values of the running resistance of the Aframax tanker

Based on the obtained value of the propeller thrust in terms of the energy balance with the power of the power plant, we find that the actual resistance to the movement of the vessel is 2 times less than according to the previously carried out theoretical calculation of the hydrodynamic resistance to the movement of the Aframax tanker (see the previous article).

That is, the actual streamlining of a rather blunt-nosed tanker turns out to be much better than according to the supposed rough model of the flow around a wedge-shaped bow with an angle of 40 degrees to the course.

As a demonstration of the hydrodynamics of the flow around bodies of various shapes, it is interesting to consider the known reference values of resistance when flowing around reference obstacles (see tab. Fig. 16-17)

So the greatest interest is the comparison of the flow resistance around a flat disk (1.17) and a hemisphere (0.38).

Differences in the resistance to flow around these two bodies of the same section reaches the ratio

K=1.17/0.38=3.09.

To obtain the same resistance, it is necessary to reduce the area of a flat disk by 3 times, which is equivalent to a decrease in the diameter of a flat disk by 3 ^ 0.5 = 1.73 times, or Dd / Dsh = 1 / 1.73 = 0.58.

It turns out that in the submarine flow mode, the “water tip” in the nose deceleration zone of the flow is 0.58 of the hull diameter, and the rest of the nose cone is inside the deceleration zone behind the separation flows from the edges of the disk. In this retarded zone behind the disk, zero resistance to movement through the water can be obtained by hiding behind the separation flows from these edge sections of the bow of the submarine.

That is, the drawn picture of the “knight’s helmet” with the “water tip” of stagnant water on the blunt bow of the submarine turned out to be very close to reality (see Fig. 20).

The zone of turbulent shadow behind the disk, where the submarine’s hull can be placed, is clearly visible in the drawing from the textbook (see Fig. 21).

Fig.20. The distribution of pressure and the shape of water flows around the bow of a submarine on the move in a submerged position.

Fig.21. A page from a textbook with a drawing of various modes of fluid flow around a disk. The “water point” in the center line deceleration zone is clearly visible in all figures. In figure (D), at high Reynolds numbers, a void is visible behind the disk, where the water flows bent by the disk do not flow, it is in this void that the submarine hull with low underwater resistance is placed. For a submarine with a diameter of 20 m at a speed of 7 m/s (14 knots), the Reynolds number is about Re=140 million, and for an Aframax tanker with a width of 42 m and a speed of 7 m/s, the number is Re=300 million, that is, for all of them, it is the mode (D) with cavities behind the jets of separated flows.

At extremely high speeds of the disc moving through the water (speed 100 m/s or more), a cavitation cavity is formed behind the disc with rarefied water vapor at a pressure of 1-2% of the atmospheric pressure.

Inside this cavitation cavity, you can even place a rocket that will fly through the water in this empty bag behind the supercavitating plate.

Such a “torpedo missile” with the name “Shkval” was indeed created back in the USSR (see fig. 22-23). She could fly underwater at a speed of 100m/s for a distance of 10km (100 seconds). True, she did not have much success in battles due to poor controllability and high visibility in motion, which greatly unmasked the submarine that launched her.

Supercavitating bullets for underwater firearms had much greater applicability. So special elongated underwater bullets fly through the water in the same cavitation bubble, while the resistance to the flight of the bullet is greatly reduced and the range of effective shooting under water is sharply increased (Fig. 24-25)