JP7206604B2 - thermal controller - Google Patents

Description

The present invention relates to a heat control device and a heat control method for controlling a heat supply destination in an apparatus having an internal combustion engine.

2. Description of the Related Art In a moving body such as a vehicle, a heat transfer medium is circulated through each part of the moving body to adjust the temperature of each part. Patent Literature 1 discloses a device that switches between supplying exhaust heat from the engine and heat stored in a heat accumulator to warm up the engine and transmission, or supplying it to a generator, based on fuel efficiency.

JP 2011-190750 A

In the conventional system, after the exhaust heat from the engine is recovered, the heat transfer medium heat-exchanged with the exhaust heat circulates in a heat loop passing through various parts in the vehicle. Therefore, even when it is necessary to store exhaust heat, the heat transfer medium circulates in a heat loop passing through various parts in the vehicle, so that heat is radiated during circulation, resulting in poor heat storage efficiency.

Accordingly, the present invention has been made in view of these points, and it is an object of the present invention to provide a heat control device and a heat control method capable of improving heat storage efficiency in an apparatus having an internal combustion engine.

A heat control device according to a first aspect of the present invention includes a heat storage unit that stores heat given to a heat transfer medium from an engine of a mobile body, a recovery unit that recovers exhaust heat from the engine of the mobile body, and the heat storage unit. a first mode of supplying a heat transfer medium warmed by heat stored in a heat transfer medium to the engine and supplying the heat transfer medium heat-exchanged with the engine to the heat storage part; a switching unit for switching between a second mode in which the heat transfer medium warmed by the heat recovered by the recovery unit is supplied to the heat storage unit without supplying the heat transfer medium to the engine.

The heat control device further includes a heater unit that performs heat exchange between air in the interior of the moving body and a heat transfer medium, and the switching unit is configured to exchange heat with the engine in the first mode. The exchanged heat transfer medium may be supplied to the heat storage section after heat exchange with the indoor air in the heater section.

The switching unit includes a first valve that switches between supplying the engine with the heat transfer medium released from the heat storage unit or supplying the heat transfer medium that has passed through the heater unit, and a first valve that passes through the heater unit. A second valve for switching between supplying the heat transfer medium to the heat storage unit and supplying the heat transfer medium to the engine of the moving body may be provided.

The switching unit includes a third valve that switches between supplying the heat transfer medium released from the heat storage unit to the engine and supplying the heat transfer medium released from the heat storage unit to the recovery unit; 1. Switches between supplying the heat transfer medium sent from the heater section via the valve to the heat storage section and supplying the heat transfer medium warmed by the heat recovered by the recovery section to the heat storage section. 4 valves.

The switching unit includes a fifth valve that switches between supplying the heat transfer medium released from the heat storage unit to the engine and supplying the heat transfer medium released from the heat storage unit to the recovery unit; a sixth valve for switching between supplying the heat transfer medium sent from the unit to the recovery unit and supplying the heat transfer medium released from the heat storage unit to the recovery unit; and a seventh valve for switching whether to supply the heat transfer medium to the engine.

The thermal control device causes the switching unit to operate in the first mode until a predetermined time elapses after the engine starts, and after the predetermined time elapses after the engine starts, and a control unit that operates the switching unit in the second mode.

The heat control device further includes a first temperature detection unit that detects the temperature of the heat transfer medium released from the heat storage unit, and while the temperature detected by the first temperature detection unit is equal to or higher than a predetermined threshold, further comprising a control unit that operates the switching unit in the first mode, and operates the switching unit in the second mode after the temperature detected by the first temperature detection unit becomes less than the predetermined threshold value. good too.

The heat control device further includes a second temperature detection unit that detects the temperature of the heat transfer medium warmed by the heat collected by the recovery unit, and the control unit detects the temperature detected by the first temperature detection unit. is equal to or higher than the temperature detected by the second temperature detection unit, the switching unit is operated in the first mode, and the temperature detected by the first temperature detection unit is the temperature detected by the second detection unit. The switching unit may be operated in the second mode after becoming less than.

The thermal control device may further comprise a pump that, in the second mode, delivers a heat transfer medium from the recovery section to the heat storage section and stops operating in the first mode.

A heat control method according to a second aspect of the present invention is executed by a computer and supplies a heat transfer medium released from a heat storage unit storing heat given to a heat transfer medium from an engine of a mobile body to the engine of the mobile body. a first step of supplying the heat transfer medium heat-exchanged with the engine to the heat storage unit in a first mode; and the heat transfer medium released from the heat storage unit after the first step. is not supplied to the engine, and the heat transfer medium warmed by the heat recovered by the recovery unit for recovering the exhaust heat from the engine of the moving body is supplied to the heat storage unit. , has

ADVANTAGE OF THE INVENTION According to this invention, it is effective in the ability to improve the heat storage efficiency in a moving body.

1 is a diagram showing the configuration (first mode state) of the heat control device of the first embodiment; FIG. It is a figure which shows the structure (state of 2nd mode) of the thermal control apparatus of 1st Embodiment. 4 is an operation flowchart of the heat control device of the first embodiment; FIG. 10 is a diagram showing the configuration (state of the first mode) of the heat control device of the second embodiment; FIG. 10 is a diagram showing the configuration (second mode state) of the heat control device of the second embodiment;

<First embodiment>
[Basic Configuration of Thermal Control Device 1]
1 and 2 are diagrams showing the configuration of a heat control device 1 according to the first embodiment. 1 shows the thermal control device 1 in the first mode, and FIG. 2 shows the thermal control device 1 in the second mode. The heat control device 1 is mounted on a vehicle, which is a type of moving body. The solid arrows in FIG. 1 indicate the direction in which the heat transfer medium in the vehicle flows through the pipes. The heat-carrying medium is, for example, cooling water. In this specification, a system in which a heat-carrying medium flows through tubes is sometimes referred to as a "thermal loop."

The heat control device 1 includes an engine 11, a radiator 12, a heater section 13, a heat accumulator 14, a collector 15, a switching section 16, a control section 17, a pump 18, a temperature sensor 21, a temperature sensor 22. The switching unit 16 has a first valve 161 , a second valve 162 , a third valve 163 and a fourth valve 164 .

In the heat loop of the first mode shown in FIG. 1, heat is generated in the order of heat accumulator 14→third valve 163→first valve 161→engine 11→heater section 13→second valve 162→fourth valve 164→heat accumulator 14. A conveying medium flows. A part of the heat transfer medium entering the engine 11 flows to the radiator 12 while the engine is warming up, but the flow is stopped by the thermostat and the rest flows to the heater section 13 .

In the second mode shown in FIG. 2, there are two thermal loops. In the first heat loop, the heat transfer medium flows in order of heat accumulator 14→third valve 163→collector 15→fourth valve 164→heat accumulator 14. FIG. In the second heat loop, the heat transfer medium flows in the order of engine 11→heater section 13→second valve 162→first valve 161→engine 11. FIG.

[Configuration and Operation of Heat Control Device 1]
The configuration and operation of each part of the heat control device 1 will be described below.
The engine 11 generates power for driving the vehicle. If the vehicle in which thermal control device 1 is installed is a commercial vehicle such as a truck or bus, engine 11 is a diesel or gasoline engine. The radiator 12 releases heat generated by the engine 11 . A pipe is provided between the engine 11 and the radiator 12 for circulating the heat transfer medium.

The heater part 13 performs heat exchange between the air inside the vehicle and the heat transfer medium. When the temperature of the heat transfer medium is higher than the temperature of the air in the room, the heater unit 13 raises the temperature in the room by releasing the air warmed by the heat of the heat transfer medium into the room. A user can set the temperature in the room using an operation unit provided on an instrument panel of the vehicle. The heater unit 13 operates so that the temperature in the room reaches a set temperature under the control of the control unit 17 .

The heat accumulator 14 stores heat given to the heat transfer medium from the engine 11 . The heat accumulator 14 stores heat by, for example, temporarily storing the heat transfer medium warmed by the exhaust heat of the engine 11 recovered by the recovery device 15 . The heat accumulator 14 is provided after the heater section 13 in the first mode. In the second mode, the heat accumulator 14 is provided after the recovery device 15 and stores the heat of the heat transfer medium sent out from the recovery device 15 . The heat accumulator 14 may store heat by storing the heated heat transfer medium itself.

The recovery device 15 is a heat exchanger that recovers heat generated by the vehicle and exchanges the recovered heat with a heat transfer medium. The heat recovered by the recovery device 15 is, for example, exhaust heat from the engine 11 or heat discharged from an EGR (Exhaust Gas Recirculation) cooler. Note that the collector 15 may have a cooling device that operates under the control of the controller 17 in order to prevent the heat transfer medium from boiling in the second mode.

The switching unit 16 switches between the first mode shown in FIG. 1 and the second mode shown in FIG. Specifically, in the first mode, the switching unit 16 supplies the heat transfer medium warmed by the heat stored in the heat accumulator 14 to the engine 11 and switches the heat transfer medium heat exchanged with the engine 11 to , heat exchange with indoor air in the heater section 13 and then supplied to the heat accumulator 14 . In addition, in the second mode, the switching unit 16 does not supply the heat transfer medium warmed by the heat accumulated in the heat accumulator 14 to the engine 11, but stores the heat transfer medium warmed by the heat collected by the collector 15. 14.

More specifically, the first to fourth valves 161 to 164 are three-way valves that operate as follows under the control of the control section 17.
The first valve 161 switches between supplying the heat transfer medium warmed by the heat accumulated in the heat accumulator 14 to the engine 11 and supplying the heat transfer medium that has passed through the heater section 13 to the engine 11 . The second valve 162 switches between supplying the heat transfer medium that has passed through the heater section 13 to the heat accumulator 14 and supplying it to the engine 11 of the vehicle via the first valve 161 .

The third valve 163 supplies the heat transfer medium warmed by the heat collected by the collector 15 to the engine 11 via the first valve 161, or supplies the heat transfer medium warmed by the heat accumulated by the heat accumulator 14. is supplied to the collector 15. The fourth valve 164 supplies the heat transfer medium sent from the heater section 13 via the second valve 162 to the heat storage device 14, or transfers the heat transfer medium warmed by the heat recovered by the recovery device 15 to the heat storage device. 14 is switched.

The control section 17 controls each section of the heat control device 1 . The control unit 17 has, for example, a CPU (Central Processing Unit), a ROM (Read Only Memory), and a RAM (Random Access Memory). The control unit 17 executes a program stored in the ROM to perform control for switching the flow path of the heat transfer medium. The control unit 17 sets the switching unit 16 to the first position until a predetermined time has elapsed since the engine 11 started (for example, until all the heat transfer medium stored in the heat storage device 14 is discharged). mode, and after a predetermined time has elapsed since the engine 11 was started, the switching unit 16 is operated in the second mode.

A pump 18 is provided between the third valve 163 and the collector 15 to generate the force for pumping the heat transfer medium. The pump 18 is deactivated and non-functional in the first mode. The pump 18 in the second mode generates power for sending the heat-carrying medium from the collector 15 via the third valve 163 to the heat accumulator 14 .

The temperature sensor 21 is a first temperature detection section that detects the temperature of the heat transfer medium released from the heat accumulator 14 . The heat transfer medium discharged from the heat accumulator 14 may be a heat transfer medium warmed by the heat stored in the heat accumulator 14, or a pre-warmed heat transfer medium stored in the heat accumulator 14. good too. The temperature sensor 22 is a second temperature detection section that detects the temperature of the heat transfer medium warmed by the heat of the collector 15 .

[Control of switching unit 16]
Details of the operation of the control unit 17 controlling the switching unit 16 will be described below.
The control unit 17 controls the first to fourth valves 161 to 164 in the first mode until a predetermined time has elapsed since the engine started.

Specifically, in the first mode, the controller 17 controls the first valve 161 so as to supply the heat transfer medium released from the heat accumulator 14 to the engine 11 . The control unit 17 controls the second valve 162 so that the heat transfer medium that has passed through the heater unit 13 is supplied to the heat accumulator 14 . The control unit 17 controls the third valve 163 so as to supply the heat transfer medium released from the heat accumulator 14 to the engine 11 via the first valve 161 . The control unit 17 controls the fourth valve 164 so as to supply the heat transfer medium sent from the heater unit 13 via the second valve 162 to the heat accumulator 14 .

The control unit 17 controls the first to fourth valves 161 to 164 in the second mode after a predetermined time has elapsed since the engine started. Specifically, in the second mode, the control unit 17 controls the first valve 161 so as to supply the engine 11 with the heat transfer medium that has passed through the heater unit 13 and the second valve 162 . The control unit 17 controls the second valve 162 so that the heat transfer medium that has passed through the heater unit 13 is supplied to the engine 11 via the first valve 161 . The control unit 17 controls the third valve 163 so as to supply the heat transfer medium that exchanges heat with the heat storage medium of the heat storage device 14 to the recovery device 15 . The controller 17 controls the fourth valve 164 so as to supply the heat transfer medium warmed by the heat collected by the collector 15 to the heat accumulator 14 .

Here, the predetermined time is, for example, until the previously measured temperature of the heat transfer medium warmed by the heat recovered by the recovery device 15 becomes higher than the temperature of the heat transfer medium released from the heat accumulator 14. It's time for The predetermined time may be a time determined based on the temperatures detected by the temperature sensors 21 and 22 .

When using the temperatures detected by the temperature sensors 21 and 22, the control unit 17 switches the switching unit 16 while the temperature detected by the temperature sensor 21 provided in the heat accumulator 14 is equal to or higher than a predetermined threshold. The switching unit 16 may be operated in the second mode while operating in the first mode and the temperature detected by the temperature sensor 21 is less than a predetermined threshold. When the temperature detected by the temperature sensor 21 is equal to or higher than the temperature detected by the temperature sensor 22 provided in the collector 15, the control unit 17 operates the switching unit 16 in the first mode so that the temperature sensor 21 The switching unit 16 may be operated in the first mode when the detected temperature is lower than the temperature detected by the temperature sensor 22 provided in the collector 15 .

Further, the control unit 17 operates the switching unit 16 in the first mode until the warm-up of the engine 11 is completed, and operates the switching unit 16 in the second mode after the warm-up of the engine 11 is completed. may The control unit 17 detects the timing at which the warm-up of the engine 11 ends, for example, based on the temperature of the heat transfer medium sent out from the engine 11 .

Thus, the heat control device 1 allows the control unit 17 to determine the elapsed time from the start of the engine 11 , the timing associated with the temperature of the heat transfer medium discharged from the heat storage device 14 , or the warm-up of the engine 11 . , the path of the heat transfer medium entering the heat accumulator 14 and the path of the heat transfer medium sent out from the heat accumulator 14 can be switched. Therefore, while sufficient heat is stored in the heat accumulator 14, the heat control device 1 utilizes the stored heat to warm up the engine 11 and raise the temperature of the room, and the heat in the heat accumulator 14 has decreased. By storing the heat recovered by the recovery device 15 in the heat storage device 14 at this time, the heat storage efficiency in the moving body can be improved.

Note that the control unit 17 may determine the timing of switching the thermal loop mode based on the external environment. After the engine 11 has started, the control unit 17 controls the temperature at the timing based on the difference between the outside air temperature detected by a temperature sensor (not shown) and the temperature detected by the temperature sensor 21 provided in the heat accumulator 14. , to switch the source of the heat-carrying medium.

Specifically, the greater the difference between the outside air temperature and the temperature detected by the temperature sensor 21, the longer it takes for the heat transfer medium to be warmed by the heat recovered by the recovery device 15. Lengthen the time required to switch from the first mode to the second mode. By doing so, the heat control device 1 can utilize the heat accumulator 14 in a manner suitable for the external environment.

[Operation Flowchart of Thermal Control Device 1]
FIG. 3 is an operation flowchart of the control unit 17. As shown in FIG. The control unit 17 monitors whether the engine 11 has started (S11). When the engine 11 is started (YES in S11), the control unit 17 controls the switching unit 16 to supply the heat transfer medium released from the heat accumulator 14 to the engine 11, thereby controlling the first heat transfer medium shown in FIG. A mode state is set (S12).

The control unit 17 monitors the temperature of the heat transfer medium released from the heat storage device 14 while supplying the heat transfer medium released from the heat storage device 14 to the engine 11 (S13). For example, when the control unit 17 determines that the temperature of the heat transfer medium released from the heat accumulator 14 has fallen below a predetermined threshold value (YES in S13), the heat accumulator 14 and the engine 11 are separated, and the heat transfer medium is recovered. The switching unit 16 is controlled to supply the heat transfer medium warmed by the heat of the vessel 15 to the heat accumulator 14, thereby switching to the second mode state shown in FIG. 2 (S14). When the engine 11 stops (YES in S15), the control unit 17 terminates the process.

[Effect of heat control device 1]
As described above, in the heat control device 1, in the first mode, the control unit 17 supplies the heat transfer medium released from the heat accumulator 14 to the engine 11 and exchanges heat with the engine 11. The switching unit 16 is controlled so as to supply the heat transfer medium to the heat accumulator 14 . In the second mode, the control unit 17 does not supply the heat transfer medium released from the heat storage device 14 to the engine 11, but supplies the heat transfer medium warmed by the heat recovered by the recovery device 15 to the heat storage device 14. The switching unit 16 is controlled so as to In this way, the heat control device 1 stores the heat recovered by the recovery device 15 while the heat storage device 14 is disconnected from the engine 11 in the second mode, so that the heat recovered by the recovery device 15 can be efficiently It can store heat.

In addition, for example, the control unit 17 is controlled when a predetermined time has elapsed since the engine 11 was started, when the temperature of the heat transfer medium released from the heat accumulator 14 is below a threshold value, or when the engine 11 is warmed up. is completed, the switching unit 16 is switched from the first mode to the second mode. By doing so, the heat stored in the heat accumulator 14 can be effectively used, so that the heat utilization efficiency in the vehicle can be improved.

In particular, in the second mode, the heat loop including the collector 15 is as short as the heat accumulator 14→the third valve 163→the collector 15→the fourth valve 164→the heat accumulator 14, so the heat collected by the collector 15 is less than the amount of heat transfer medium circulating in the first mode heat loop. Therefore, the heat recovered by the recovery device 15 can be effectively stored in the heat storage device 14 .

<Second embodiment>
4 and 5 are diagrams showing the configuration of the heat control device 2 according to the second embodiment. 4 shows the thermal control device 2 in the first mode, and FIG. 5 shows the thermal control device 2 in the second mode.

In the heat control device 1 according to the first embodiment, the switching section 16 has the first valve 161 , the second valve 162 , the third valve 163 and the fourth valve 164 . On the other hand, the heat control device 2 according to the second embodiment has a switching section 23 instead of the switching section 16, and the switching section 23 includes a fifth valve 231, a sixth valve 232, a seventh valve 233 and a It differs from the thermal control device 1 in that it has a pump 234 . The states of the fifth valve 231 , the sixth valve 232 , the seventh valve 233 and the pump 234 are switched under the control of the controller 17 .

The conditions for switching the control unit 17 of the heat control device 2 between the first mode and the second mode are the same as those of the heat control device 1 according to the first embodiment. For example, the control unit 17 switches to the first mode for a predetermined time from when the engine 11 is started until the heat transfer medium stored in the heat accumulator 14 is discharged, and the heat transfer medium stored in the heat accumulator 14 is transferred. After the medium is discharged, the second mode is entered.

The fifth valve 231 is a three-way valve that switches between supplying the heat transfer medium released from the heat storage device 14 to the engine 11 and supplying the heat transfer medium released from the heat storage device 14 to the collector 15 . The sixth valve 232 is a three-way valve that switches between supplying the heat transfer medium sent from the heater section 13 to the recovery device 15 and supplying the heat transfer medium released from the heat storage device 14 to the recovery device 15 . be. The seventh valve 233 is an on/off valve that switches whether to supply the heat transfer medium sent from the heater section 13 to the engine 11 . The pump 234 stops operating in the first mode and generates a conveying force for conveying the heat-carrying medium released from the heat accumulator 14 toward the collector 15 in the second mode.

In the heat loop of the first mode shown in FIG. 4, the heat transfer medium flows in order of heat accumulator 14→fifth valve 231→engine 11→heater section 13→sixth valve 232→collector 15→heat accumulator 14. FIG. In the second mode shown in Figure 5, there are two thermal loops. In the first heat loop, the heat transfer medium flows in order of heat accumulator 14→fifth valve 231→pump 234→sixth valve 232→collector 15→heat accumulator 14. FIG. In the second heat loop, the heat transfer medium flows in the order of engine 11→heater section 13→seventh valve 233→engine 11 .

Thus, in the thermal control device 2, switching between the first mode and the second mode can be performed using a smaller number of valves than in the thermal control device 1, so that the thermal control device 2 can be realized at a lower cost than the thermal control device 1. be able to.

Although the present invention has been described above using the embodiments, the technical scope of the present invention is not limited to the scope described in the above embodiments. It is obvious to those skilled in the art that various modifications or improvements can be made to the above embodiments. It is clear from the description of the scope of claims that forms with such modifications or improvements can also be included in the technical scope of the present invention. For example, in the above description, the mobile object is a vehicle, but the mobile object is not limited to a vehicle, and the present invention can also be applied to other mobile objects such as aircraft, ships, and trains. . Further, the moving body according to the present invention does not necessarily have a function of moving, and may be any device having an internal combustion engine.

1 Heat control device 11 Engine 12 Radiator 13 Heater unit 14 Heat accumulator 15 Collector 16 Switching unit 17 Control unit 18 Pumps 21 to 22 Temperature sensor 161 First valve 162 Second valve 163 Third valve 164 Fourth valve 23 Switching unit 231 fifth valve 232 sixth valve 233 seventh valve 234 pump

Claims (5)

a heat storage unit that stores heat given to the heat transfer medium from the engine of the moving body;
a recovery unit that recovers exhaust heat from an engine of the moving body;
a first mode in which a heat transfer medium warmed by the heat stored in the heat storage unit is supplied to the engine and the heat transfer medium heat-exchanged with the engine is supplied to the heat storage unit; a switching unit for switching between a second mode in which the released heat transfer medium is not supplied to the engine and the heat transfer medium warmed by the exhaust heat collected by the recovery unit is supplied to the heat storage unit;
a heater unit for exchanging heat between air in the moving body and a heat transfer medium;
has
The switching unit is
a fifth valve that is a three-way valve that switches between supplying the heat transfer medium released from the heat storage unit to the engine and supplying the heat transfer medium released from the heat storage unit to the recovery unit;
a sixth valve that is a three-way valve that switches between supplying the heat transfer medium sent from the heater section to the recovery section and supplying the heat transfer medium released from the heat storage section to the recovery section;
a seventh valve that is an on/off valve that switches whether to supply the heat transfer medium sent from the heater section to the engine;
a pump which is provided between the fifth valve and the sixth valve and which, in the second mode, sends a heat transfer medium from the recovery section to the heat storage section and stops operating in the first mode; ,
has
In the first mode, when the seventh valve is off, a heat loop is formed in which the heat transfer medium flows through the heat storage section, the fifth valve, the engine, the heater section, the sixth valve, and the recovery section in this order. and in the second mode, a first heat loop in which a heat transfer medium flows in the order of the heat storage section, the fifth valve, the pump, the sixth valve, and the recovery section, and the seventh valve is on. a second heat loop is formed in which a heat transfer medium flows in the order of the engine, the heater section, and the seventh valve in this state, and the first heat loop is shorter than the heat loop in the first mode ; The heat control device, wherein the amount of the heat transfer medium warmed by the heat recovered by the recovery unit in the second mode is less than the amount of the heat transfer medium circulated in the first mode. In the first mode, the switching unit supplies the heat transfer medium heat-exchanged with the engine to the heat storage unit after heat-exchanging with the indoor air in the heater unit.
The thermal control device of claim 1. The switching unit is operated in the first mode until a predetermined time elapses after the engine starts, and the switching unit is operated in the first mode after the predetermined time elapses after the engine starts. further comprising a control unit that operates in the second mode;
3. A thermal control device according to claim 1 or 2 . further comprising a first temperature detection unit that detects the temperature of the heat transfer medium released from the heat storage unit;
While the temperature detected by the first temperature detection unit is equal to or higher than a predetermined threshold, the switching unit is operated in the first mode, and the temperature detected by the first temperature detection unit is less than the predetermined threshold. further comprising a control unit that operates the switching unit in the second mode later,
4. A thermal control device according to any one of claims 1-3 . a first temperature detection unit that detects the temperature of the heat transfer medium released from the heat storage unit;
a second temperature detection unit that detects the temperature of the heat transfer medium warmed by the heat recovered by the recovery unit;
While the temperature detected by the first temperature detection unit is equal to or higher than the temperature detected by the second temperature detection unit, the switching unit is operated in the first mode, and the temperature detected by the first temperature detection unit is a control unit that operates the switching unit in the second mode after the temperature becomes lower than the temperature detected by the second temperature detection unit;
further having
4. A thermal control device according to any one of claims 1-3 .

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