CN116882053A - Energy efficiency coupling optimization method based on take-off and taxi phases of electric aircraft on water - Google Patents
Energy efficiency coupling optimization method based on take-off and taxi phases of electric aircraft on water Download PDFInfo
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Abstract
The invention relates to the technical field of new energy aviation electrodynamic systems, in particular to an energy efficiency coupling optimization method based on a take-off and taxi stage of an electric aircraft on water. Comprising the following steps: the structure of an aircraft electrodynamic system is optimized by solving the optimal pitch angle of the propeller; wherein said solving for the optimal pitch angle of the propeller comprises: firstly, establishing an energy consumption equation of an electric power system for completing a take-off and taxi task of an airplane; and secondly, establishing an optimization objective function of the electrodynamic system. The invention provides an energy efficiency optimization method suitable for a fixed-pitch propeller electric power system of an electric aircraft on water, aiming at the electric power system of the electric aircraft on water in a take-off and taxi stage, which can obviously reduce the system loss of the aircraft in the take-off and taxi stage and increase the endurance time of the aircraft.
Description
Technical Field
The invention discloses the technical field of new energy aviation electrodynamic force systems, in particular to an energy efficiency coupling optimization method based on a take-off and taxi stage of an electric aircraft on water.
Background
The electric aircraft on water is used as a new energy aircraft for cleaning pollution, namely a fixed wing electric aircraft which can take off, land and park on the water surface, and has unique advantages in the aspects of offshore rescue, sightseeing tour and the like compared with an oil-driven aircraft; with the great development of the emergency rescue system and the tourism industry in China, the electric aircraft on water has been paid great attention to the aviation field in China. However, the method is affected by relatively low energy density of the current lithium storage battery, and the duration of the electric water plane is short, so that the application and popularization of the electric water plane are directly restricted.
The electric aircraft on water is different from the electric aircraft on land, the electric aircraft on land has shorter duration in the take-off and taxiing stage, and the energy consumption is smaller and can be ignored generally; the water electric aircraft is more complex in process and more in energy consumption due to the influence of factors such as water kinetic resistance in the take-off and taxiing stage. Because the fixed pitch propeller has simple structure and convenient maintenance, the fixed pitch propeller is usually selected for the electric water plane, and the high-efficiency range of the fixed pitch propeller is narrower, so that the electric power system of the electric water plane has lower efficiency in the take-off and taxiing stage, and has larger energy consumption, and the cruising ability and safety of the electric water plane are directly influenced.
Disclosure of Invention
In view of the above, the invention discloses an energy efficiency coupling optimization method based on the take-off and taxi phases of an electric aircraft on water, so as to increase the endurance time of the aircraft and ensure that the aircraft cannot be excessively worn due to an aircraft electrodynamic system.
The technical scheme provided by the invention is as follows: an energy efficiency coupling optimization method based on a take-off and taxi phase of an electric aircraft on water comprises the following steps: the structure of an aircraft electrodynamic system is optimized by solving the optimal pitch angle of the propeller;
wherein said solving for the optimal pitch angle of the propeller comprises: firstly, establishing an energy consumption equation of an electric power system of the energy required by the aircraft to finish a take-off and taxi task; and secondly, establishing an optimization objective function of the electrodynamic system.
Further, the aircraft powertrain completes the total energy consumption E of one-time flight taxiing task g Can be expressed as:
wherein: the output power requirements of the electric power system in the take-off and taxiing stage are respectively E, wherein the electric power system is divided into a sailing stage, a transitional taxiing stage, a high-speed taxiing stage and a flying and leaving stage g_1 ,E g_2 ,E g_3 ,E g_4 The method comprises the steps of carrying out a first treatment on the surface of the The efficiency of the motor, the controller and the propeller in different stages of the take-off and taxiing of the airplane is eta respectively m_x、 η c_x And eta p_x The method comprises the steps of carrying out a first treatment on the surface of the The sailing stage, the transitional sliding stage, the high-speed sliding stage and the flying off-water stage are the sliding stages of the airplane determined according to the pitch angle of the airplane;
the optimization objective function of the electrodynamic system is as follows:
wherein: e (E) min The minimum energy consumption of the electric power system when the aircraft completes one take-off and taxiing task is realized; e (E) g The total energy consumption of the aircraft when finishing one take-off taxi task is provided.
Further, hydrodynamic resistance T of the sailing stage w From viscous drag R and wave-making drag R W Two parts, wherein the viscous resistance comprises friction resistance and shape resistance;
defining B as the width of the pontoon, and determining according to the parameters of the seaplane; by N p The number of pontoons is R e Is Reynolds number, v w For the navigational speed of the airplane to water, the navigational speed v of the airplane is used for carrying out representation calculation on the water area with low static water or water flow speed, and the viscosity coefficient mu of the water w ＝1.19*10 -6 m 2 S (sea water), ρ w =997 kg/m3 is the density of water;
coefficient of friction C for water f The calculation can be performed by adopting the formula of the Planta-Xu Liting:
further, the viscous drag R can be calculated by the following formula
Defining coefficient K according to formula of wave making resistance calculation 0 And note gravitational acceleration g=9.8 m/s 2 Then:
building a coordinate system for the pontoon, wherein xi= (x, y, z) is the coordinates of a source point on the pontoon surface; the potential function of a source sink can be expressed as:
wherein S is the wet surface area of the pontoon under the still water, sigma is the source potential intensity distributed on the pontoon surface, c w Is the intersection of the water surface and the pontoon surface, cos (x, n) is the cosine of the angle between the pontoon surface normal and the x-axis, dw=dssin (y, n), where ds is the infinitesimal on the water line, where f x G is green's function, which is the pontoon surface equation.
Defining alpha as a mathematical intermediate variable, and physically representing an included angle between the travelling direction of the primitive wave and the travelling direction of the pontoon, wherein the calculation method of the wave-making resistance is as follows:
wherein S is the wet surface area of the pontoon under the still water, H 1 P is the pontoon surface pressure distribution and i is the imaginary unit as a function of kochn.
From viscous drag R and wave-making drag R w Can obtain the sailing water resistance T w _ 1 Is that
T w_1 ＝R+R W
The thrust required to be output by the propeller can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
Wherein T is p_1 Outputting thrust for the propeller; w (W) p_1 Is the propeller power demand; r is R p Is the radius of the propeller; c (C) T The thrust coefficient of the propeller is characterized by the influence of factors such as pitch angle, wing profile, number of blades and the like on the thrust of the propeller, beta is the power coefficient of the propeller, and the beta value depends on the pitch angle, the wing profile, the number of blades and the like; c of propeller under fixed pitch angle T And the variation characteristic of beta along with the rotating speed of the propeller can be determined by a propeller wind tunnel test; ρ is air density, which can be approximately 1.29kg/m due to the limited low-altitude flight of the electric water aircraft below 3000m 3 ；n p Solving hidden functions according to the two formulas to obtain the output power of the propeller for the rotating speed of the propeller;
the total energy consumption of an electric aircraft during the voyage phase can be expressed as:
wherein E is g_1 T is the total energy consumption in the sailing phase g_1 For the time of sailing phase, W p_1 Power required for aircraft operation during sailing phase, where η m_1 、η c_1 And eta p_1 The efficiency of the motor, the controller and the propeller of the aircraft in the sailing stage can be obtained through the test flight data of the aircraft in the sailing stage.
Further, hydrodynamic drag T in the over-taxiing phase w_2 From viscous drag R and wave-making drag R W Two parts, wherein the viscous drag comprises frictional drag R f And shape resistance R p ；
Coefficient of friction C for water f The mulberry equation is used at this stage to calculate:
water resistance T during excessive taxiing w 2 From viscous drag R and wave-making drag R W Adding to obtain
T w_2 ＝R+R W
Assuming that the acceleration of the aircraft during the over taxiing phase is a 2 The required output thrust of the propeller can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
The total energy consumption of the aircraft during the over taxiing phase may be expressed as
Wherein E is g_2 To total energy consumption in the excessive coasting phase, t g_2 For excessive coasting periodW is the same as p_2 Power required for aircraft operation during excessive taxiing phase, where η m_2 、η c_2 And eta p_2 The efficiency of the motor, the controller and the propeller of the aircraft in the excessive taxiing stage can be obtained through test flight data of the aircraft in the excessive taxiing stage.
During the high speed slip phase T D Aerodynamic drag for an aircraft can be expressed as:
wherein S is the area of the wing; c (C) D Is the aerodynamic drag coefficient; m is Mach number, the ratio of aircraft speed to sound velocity; m is M l Mach number for incoming flow, i.e., mach number of far-field gas; m is M ln For local mach number, γ is the gas specific heat ratio, γ=1.4 for air;
carrying out stress analysis on the aircraft, wherein θ is the pitch angle in the take-off and taxiing stage;the included angle between the thrust line of the electrodynamic system and the lower construction line of the aircraft can be approximately determined after the aircraft is shaped; m is the aircraft take-off quality; v is the taxiing speed of the aircraft in the horizontal direction; v fl Is the flying speed of the airplane in the axial direction, which is approximately equal to the advancing speed of the propeller, t 2 A is the time of ending the last stage 3 Acceleration during the high-speed coasting phase; r is taken s The total resistance of the aircraft in the high-speed sliding stage is received;
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
The energy consumption of an aircraft in the high speed glide phase can be expressed as:
wherein E is g_3 For total energy consumption during the high-speed coasting phase, t g_3 For the time of the high-speed coasting phase, W p_3 Power required for aircraft operation during high speed taxiing phase, where η m_3 、η c_3 And eta p_3 The efficiency of the motor, the controller and the propeller of the aircraft in the high-speed sliding stage can be obtained through test flight data of the aircraft in the stage.
In the flying water-leaving stage, the calculation formula of the water intake dynamic resistance is a Frude formula:
wherein l b Is the pontoon length, t w Is the water temperature;
the aerodynamic drag calculation method and the high-speed sliding stage are similar as follows:
the power calculation is carried out according to a thrust power calculation formula, and the thrust and power requirements output by the propeller can be expressed as follows according to the phyllanthin theory
The total energy consumption of the electric aircraft in the flying and leaving stage is calculated by the following formula:
wherein E is g_4 For total energy consumption, t, of the fly-away stage g_4 To fly away from the waterTime of flight phase, W p_4 The power required for the operation of the aircraft in the fly-away stage, where eta m_4 、η c_4 And eta p_4 The efficiency of the motor, the controller and the propeller of the aircraft in the stage of flying away from the water can be obtained through the test flight data of the aircraft in the stage.
Further, the solving the optimal pitch angle of the propeller specifically includes:
step one, assuming that the minimum pitch angle of the propeller is alpha min The maximum pitch angle is alpha max The calculated step length of the pitch angle is delta alpha, and delta alpha is less than or equal to alpha min/10;
step two, assume n= [ (α) max -α min )/Δα]Rounding up, taking n=1, pitch angle α of propeller 1 ＝α min Calculating the energy consumption of the electric propulsion system for completing the primary flight task by the electric power system;
step three, taking n=n+1, and the pitch angle alpha of the propeller n ＝α n-1 +delta alpha, calculating energy consumption Es [ n ] of electric propulsion system for completing one-time flight task by using electric power system]；
Step four, judging Es [ n-1 ]]≤Es[n]Whether or not it is true, if so, E min ＝E s [n-1] The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, E min ＝E s [n] ；
Step five, judging alpha n ≤α max If yes, returning to the third step, and re-calculating; otherwise return E min ，
E min The minimum energy consumption of the aircraft for completing one take-off task is the minimum pitch angle of the system energy consumption, and the optimal pitch angle is obtained.
The invention provides an energy efficiency coupling optimization method based on a take-off and taxi stage of a water electric aircraft, which is suitable for a fixed pitch propeller electric power system of the water electric aircraft aiming at the take-off and taxi stage of the electric power system of the water electric aircraft, and can obviously reduce the system loss of the aircraft in the take-off and taxi stage and increase the endurance time of the aircraft.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure of the invention as claimed.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the description of the embodiments or the prior art will be briefly described below, and it will be obvious to those skilled in the art that other drawings can be obtained from these drawings without inventive effort.
FIG. 1 is a graph showing pitch angle and hydrodynamic drag variation of an aircraft in four stages according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a preliminary stress analysis of an electric water-powered aircraft during a water takeoff taxiing phase of the aircraft provided by the disclosed embodiments of the present invention;
fig. 3 is a schematic view of the change of the waterline height in the excessive sliding stage according to the embodiment of the invention.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the invention. Rather, they are merely examples of systems consistent with aspects of the invention as detailed in the accompanying claims.
For conventional fixed pitch propeller power systems there are as follows: the method is based on the energy efficiency coupling optimization method in the take-off and taxi stage of the electric aircraft on water, and the energy consumption calculation method in the take-off and taxi stage of the electric aircraft is obtained through analyzing the water movement characteristics of the electric aircraft on water; the energy consumption of the aircraft electrodynamic force system in the take-off and taxiing stage is reduced by optimizing the pitch angle of the aircraft fixed pitch propeller, the aircraft electrodynamic force system structure is optimized, the endurance time of the aircraft is further improved, the heating value of the aircraft electrodynamic force system is reduced, the heat dissipation environment of the aircraft electrodynamic force system is improved, and the flight safety of the aircraft is ensured.
The method specifically comprises the following steps: the structure of an aircraft electrodynamic system is optimized by solving the optimal pitch angle of the propeller;
wherein said solving for the optimal pitch angle of the propeller comprises: firstly, establishing an energy consumption equation of an electric propulsion system for completing a take-off task of an aircraft; and secondly, establishing an optimization objective function of the electrodynamic system.
The hydroplane is different from the land plane, and in the process of taking off and taxiing on the water surface, the hydropneumatic characteristics of the plane in the process of taking off and taxiing on the water surface are determined by the combined action of the hydropneumatic characteristics of the plane and the motion parameters such as the hydropneumatic, the pitch angle, the lift (the draft depth of a ship) and the like which are changed along with the change of the speed due to the influence of various acting forces such as the hydrostatic force, the hydrodynamic force, the aerodynamic force and the gravity. According to the characteristics of hydrodynamic force and aerodynamic force in the take-off and taxiing process of the water plane, the whole take-off and taxiing process of the water plane can be divided into four stages: each stage has the characteristics of a sailing stage, a transitional sliding stage, a high-speed sliding stage and a flying off-water stage, and the sliding stage of the aircraft can be determined according to the pitch angle of the aircraft. The pitch angle and hydrodynamic drag changes of the aircraft in four stages are shown in fig. 1.
The speed of the sailing stage is lower, which is about 1/4 of the water leaving speed of the airplane, the motion state is like that of the ship sliding in water, the pitch angle and the water resistance are continuously increased along with the increase of the speed, and the water resistance and the speed are approximately in a linear relation;
in the transitional sliding stage, a large amount of water is accumulated at the front part of the ship body along with the increase of the speed of the airplane, the precursor breaks off, the draft of the airplane is reduced, the pitch angle and the water resistance are obviously increased, the buoyancy point is continuously moved backwards, when the buoyancy point is moved to the gravity center position, the pitch angle and the water resistance reach peak values, a first resistance peak is formed, and the pitch angle and the water resistance are gradually reduced. The speed is about 1/4 to 1/2 of the speed of the water leaving.
In the high-speed sliding stage, as the speed continues to increase, the hull is further lifted, the draft area is further reduced, the pitch angle and the water resistance of the airplane continue to be reduced, and the speed is about 1/2 to 4/5 of the off-water speed.
The water-free stage of the flying is gradually increased in sliding speed, the longitudinal inclination angle is increased, water flow flushes the bottom of the ship, the water-free resistance is increased under the action of the water-free sliding resistance, at the moment, the air resistance is continuously increased to form a second resistance peak, the water-free resistance is rapidly reduced after the water-free resistance is rapidly reduced until the aircraft becomes zero when leaving water, and the aircraft takes off and slides to finish, at the moment, the water-free speed is about between 4/5 and 1.
The aircraft take-off and taxiing stage comprises four stages of sailing, transitional taxiing, high-speed taxiing and flying off water, and the speed of the aircraft in the flying off water stage reaches v when the speed of the aircraft in the flying off water stage is 0 when the aircraft enters the sailing stage f When the aircraft leaves water, the aircraft enters a climbing stage.
According to different characteristics of the take-off and taxiing phases, the take-off phase is divided into four phases of a sailing phase, a transitional taxiing phase, a high-speed taxiing phase and a flying and water leaving phase. According to the stage that the electric water-borne aircraft takes off and taxis on water when the aircraft takes off, the electric water-borne aircraft is influenced by self gravity, propeller thrust, aerodynamic lift, aerodynamic resistance, hydrodynamic lift, hydrodynamic resistance and the like. Preliminary force analysis is performed as shown in FIG. 2
Wherein θ is the pitch angle of the aircraft, that is, the angle between the aircraft fuselage and the horizontal plane, or the elevation angle of the aircraft nose;the included angle between the thrust line of the electrodynamic system and the lower construction line of the aircraft can be approximately determined after the aircraft is shaped; m is the take-off quality of the aircraft, which means the aircraft is carried during take-offThe total weight of the belt, including the weight of the aircraft itself, the weight of the fuel, passengers, cargo, luggage, and other items. The take-off quality of an aircraft is a key parameter, has important influence on the take-off performance, fuel consumption, range and the like of the aircraft, and for an electric aircraft, the take-off quality comprises the weight of the electric aircraft, the weight of a battery pack, the weight of passengers, goods, baggage and other articles. The takeoff quality of an electric aircraft will typically be lighter than a conventional fuel-powered aircraft because the density of the fuel-cell stack required for an electric aircraft is much lower than that of fuel; t (T) p The thrust output by the propeller at the take-off stage; t (T) D Is pneumatic resistance; t (T) W Is hydrodynamic resistance; t (T) L Is an aerodynamic lift force; t (T) AL Is hydrodynamic lift.
The sailing stage is the first stage of the take-off and taxiing stage, has a remarkable characteristic that the hydrodynamic lift force is negative, and the aerodynamic force is far smaller than the hydrodynamic force due to the lower sailing speed. This means that buoyancy needs to be increased to balance a significant portion of the weight of the aircraft, most of which is compensated by hydrodynamic lift, and aircraft weight is supported primarily by buoyancy, the effect of aerodynamic forces on the aircraft being negligible in this portion of the calculation. The taxiing of the aircraft at this point is similar to the navigation of a ship in water. The calculation can be performed according to a calculation method of the ship sailing in the water at a low speed.
Hydrodynamic drag T for sailing phases w From viscous drag R and wave-making drag R W Two parts, wherein the viscous drag comprises friction drag and shape drag.
Defining B as the width of the pontoon, and determining according to the parameters of the seaplane by N p The number of pontoons is R e Is Reynolds number, v w For the navigational speed of the aircraft to water, the navigational speed v of the aircraft can be used for representing and calculating the viscosity coefficient mu of the water for the water area with low static water or water flow speed w ＝1.19*10 -6 m 2 S (sea water), ρ w =997kg/m 3 is the density of water
Coefficient of friction C for water f The calculation can be performed by adopting the formula of the Planta-Xu Liting:
further, the viscous drag R can be calculated by the following formula
Defining coefficient K according to formula of wave making resistance calculation 0 And note gravitational acceleration g=9.8 m/s 2 Then:
we construct a coordinate system for the pontoon, ζ= (x, y, z) is the source point coordinate on the pontoon surface. The potential function of a source sink can be expressed as:
wherein S is the wet surface area of the pontoon under the still water, sigma is the source potential intensity distributed on the pontoon surface, c w Is the intersection line of the water purifying surface and the pontoon surface, and cos (x, n) is the cosine of the included angle between the pontoon surface normal and the x-axis. Where dw=dssin (y, n), where ds is the infinitesimal on the water line. Wherein f x G is green's function, which is the pontoon surface equation.
Defining alpha as a mathematical intermediate variable, and physically representing an included angle between the advancing direction of a basic wave (a long peak wave of simple harmonic) and the advancing direction of a pontoon, wherein the wave-making resistance is calculated by the following steps:
wherein S is the wet surface area of the pontoon under the still water, H 1 P is the pontoon surface pressure distribution and i is the imaginary unit as a function of kochn.
Water resistance T for sailing w From viscous drag R and wave-making drag R W Adding to obtain
T w_1 ＝R+R W
The calculation method of the required output thrust of the propeller is expressed by the following formula:
the power calculation is carried out according to a thrust power calculation formula, and the thrust and power requirements output by the propeller can be expressed as follows according to the phyllanthin theory
Wherein T is p_1 Outputting thrust for the propeller; w (W) p_1 Is the propeller power demand; r is R p Is the radius of the propeller; c (C) T The thrust coefficient of the propeller is characterized by the influence of factors such as pitch angle, wing profile, number of blades and the like on the thrust of the propeller, beta is the power coefficient of the propeller, and the beta value depends on the pitch angle, the wing profile, the number of blades and the like; c of propeller under fixed pitch angle T And the variation characteristic of beta along with the rotating speed of the propeller can be determined by a propeller wind tunnel test; ρ is air density, which can be approximately 1.29kg/m due to the limited low-altitude flight of the electric water aircraft below 3000m 3 ；n p And solving a hidden function according to the two formulas to obtain the output power of the propeller for the rotating speed of the propeller.
The total sailing energy of the electric aircraft in the first stage is calculated by the following formula
In E g_1 T is the total energy consumption in the sailing phase g_1 For the time of sailing phase, W p_1 For sailingThe power required for the operation of the aircraft in stages, where eta m 、η c Motor efficiency and controller efficiency, η, for each sailing phase p Is propeller efficiency.
During the excessive taxiing phase, there is a resistance peak with a corresponding speed of 'lifting speed', at this stage, an air cushion phenomenon occurs at the bottom of the pontoon, the sliding area of the rear body is reduced, the hydraulic pressure and bending moment of the rear body are correspondingly reduced, and the hydraulic pressure of the front body is continuously increased to ensure balance, so that the total hydrodynamic moment of the seaplane is suddenly increased to the maximum. The water line height will increase and then decrease during this process as shown in fig. 3.
In this excessive taxiing phase, the main characteristics are a rapid increase in pitch angle and a decrease in draft, the aerodynamic drag of the electric aircraft begins to increase rapidly, but due to the air cushion phenomenon at the bottom of the pontoon, the hydrodynamic drag is still far greater than the aerodynamic drag, and the calculation of this part can be performed by a high-speed sailing yacht model.
Hydrodynamic drag T for excessive taxiing phases w Still by viscous drag R and wave-making drag R W Two parts, wherein the viscous drag comprises friction drag and shape drag.
Coefficient of friction C for water f The calculation can be performed at this stage by using the mulberry equation:
the rest calculation method is similar to the first stage, and the sailing water resistance T w From viscous drag R and wave-making drag R W Adding to obtain
T w_2 ＝R+R W
Record a 2 The calculation method of the required output thrust of the propeller is expressed by the following formula:
the power calculation is carried out according to a thrust power calculation formula, and the thrust and power requirements output by the propeller can be expressed as follows according to the phyllanthin theory
The total sailing energy of the electric aircraft in the second stage is calculated by the following formula
Wherein E is g_2 To total energy consumption in the excessive coasting phase, t g_2 For the time of the excessive coasting period, W p_2 Power required for aircraft operation during excessive taxiing phase, where η m_2 、η c_2 And eta p_2 The efficiency of the motor, the controller and the propeller of the aircraft in the excessive taxiing stage can be obtained through test flight data of the aircraft in the excessive taxiing stage.
The pontoon portion is further lifted during the high-speed glide phase, the air cushion increases after the step break, and the draft area further decreases, wherein the hydrodynamic drag begins to decrease slowly and the aerodynamic drag begins to increase as the speed increases.
The T is D Aerodynamic drag for an aircraft can be expressed as:
wherein S is the area of the wing; c (C) D Is the aerodynamic drag coefficient; m is Mach number, the ratio of aircraft speed to sound velocity; m is M l Mach number for incoming flow, i.e. the Mach number of far field gas, i.e. the Mach number of air away from the aircraft; m is M ln Is the local Mach number, i.e., the ratio of the gas velocity to the sound velocity at a point on the aircraft surface; γ is the gas specific heat ratio, γ=1.4 for air.
Stress analysis is carried out on the aircraft, wherein theta is the longitudinal inclination angle of the take-off and taxiing stage；The included angle between the thrust line of the electrodynamic system and the lower construction line of the aircraft can be approximately determined after the aircraft is shaped; m is the aircraft take-off quality; v is the taxiing speed of the aircraft in the horizontal direction; v fl Is the flying speed of the airplane in the axial direction, which is approximately equal to the advancing speed of the propeller, t 2 A is the time of ending the last stage 3 Acceleration during the high-speed coasting phase; r is taken s Is the total drag experienced by the high speed glide phase aircraft.
The power calculation is carried out according to a thrust power calculation formula, and the thrust and power requirements output by the propeller can be expressed as follows according to the phyllanthin theory
The total sailing energy of the electric aircraft in the third stage is calculated by the following formula
Wherein E is g_3 For total energy consumption during the high-speed coasting phase, t g_3 For the time of the high-speed coasting phase, W p_3 Power required for aircraft operation during high speed taxiing phase, where η m_3 、η c_3 And eta p_3 The efficiency of the motor, the controller and the propeller of the aircraft in the high-speed sliding stage can be obtained through test flight data of the aircraft in the stage.
The water-free stage of the flying gradually increases the sliding speed, the longitudinal inclination angle increases, the water flow flushes the bottom of the ship, the water-driven resistance increases under the action of the water-driven sliding resistance, at the moment, the air resistance continues to increase to form a second resistance peak, the water-driven resistance rapidly decreases after the water-driven resistance becomes zero when the aircraft leaves water, and the aircraft takes off and slides to finish.
In this stage, the flying speed of the seaplane is 0.8-1 times of stall speed, and the wing is increased to reduce the immersed part of the pontoon to zero, so that the airplane quickly rises.
The water intake dynamic resistance calculation formula is a Froude formula:
wherein l b Is the pontoon length, t w Is the water temperature.
The aerodynamic drag calculation can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
The total energy consumption of the electric aircraft in the flying and leaving stage can be expressed as
Wherein E is g_4 To the total energy consumption of the water-leaving stage of the fly, t g_4 For the time of the water-leaving phase of flying, W p_4 The power required for the operation of the aircraft in the fly-away phase, where eta m_4 、η c_4 And eta p_4 The efficiency of the motor, the controller and the propeller of the aircraft in the stage of flying and leaving water can be obtained through the test flight data of the aircraft in the stage.
In conclusion, the energy consumption calculation method of the aircraft in the take-off and taxi stage is obtained by analyzing the water dynamic characteristics of the electric aircraft in the take-off and taxi stage; the energy consumption calculation equation of the electric power system for completing the one-time take-off and taxi task by the power system is obtained as follows:
wherein: the output power requirements of the electric power system in the take-off stage of the aircraft are divided into a sailing stage, a transitional taxiing stage, a high-speed taxiing stage and a flying water-leaving stage g_1 ,E g_2 ,E g_3 ,E g_4 The method comprises the steps of carrying out a first treatment on the surface of the The efficiency of the motor and the propeller of the controller in the plane take-off and taxiing stage is eta respectively m_x、 η c_x And eta p_x The method comprises the steps of carrying out a first treatment on the surface of the The sailing stage, the transitional sliding stage, the high-speed sliding stage and the flying off-water stage are the taking off sliding stage of the airplane which is determined according to the pitch angle of the airplane;
the optimization objective function of the aircraft electrodynamic system is as follows:
wherein: e (E) min For the minimum energy consumption of the electric power system when the aircraft completes one take-off and taxiing task, E g The total energy consumption required by the aircraft to complete one take-off taxi task.
According to the above, specifically, the solving the optimal pitch angle of the propeller may include the following steps:
step one, assuming that the minimum pitch angle of the propeller is alpha min The maximum pitch angle is alpha max The calculated step length of the pitch angle is delta alpha, and delta alpha is less than or equal to alpha min/20;
step two, assume n= [ (α) max -α min )/Δα]Rounding up, taking n=1, pitch angle α of propeller 1 ＝α min Calculating the energy consumption required by the electric power system to complete one take-off and taxi task;
step three, taking n=n+1, and the pitch angle alpha of the propeller n ＝α n-1 +delta alpha, calculating energy consumption E required by electric power system to complete one take-off and taxi task g [n]；
Step four, judging E s [n-1]≤E s [n]Whether or not it is true, if so, E min ＝E g [n-1] The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, E min ＝E g [n] ；
Step five, judging alpha n ≤α max If yes, returning to the third step, and re-calculating; otherwise return E min ，E min The minimum energy consumption of the aircraft for completing one take-off and taxi task is the propeller pitch angle alpha which is the minimum energy consumption of the aircraft in the take-off and taxi process, and the optimal pitch angle is obtained.
By applying the method provided by the embodiment, the energy efficiency of the airplane is improved: by optimizing the pitch angle of the fixed-pitch propeller of the aircraft, the energy consumption of the aircraft in the take-off and taxi stage on water is reduced, and therefore the energy efficiency of the aircraft is improved. This means that the aircraft can fly further under the same energy source, thereby increasing its value in use. Meanwhile, the endurance time of the airplane is also increased: by reducing the energy consumption during the takeoff phase, the aircraft can more efficiently utilize energy. This may extend the duration of the aircraft, enabling it to fly longer. The heating value is reduced: the heat productivity of the electrodynamic system can be reduced by reducing the energy consumption in the take-off stage, thereby reducing the heat dissipation burden of the aircraft. This may increase the life of the electric powertrain and reduce the time and cost required for cooling and maintenance. The heat dissipation environment of the electrodynamic system is improved: the optimized pitch angle scheme of the embodiment can reduce the heating value of the electric power system and optimize the structure of the electric power system. This will improve the heat dissipation environment of the electric power system, improving the performance and reliability of the electric power system. The safety of the aircraft is improved: the energy efficiency and the structure of the electric power system are optimized, so that the energy consumption of the aircraft in the take-off and taxiing stage can be reduced, and the endurance time of the aircraft is prolonged. These factors may increase the stability and reliability of the aircraft, improving flight safety.
The method is applied to the airplane, so that the precision of an airplane motor is effectively improved, the energy consumption of the airplane in the take-off process is reduced by about 10 percent compared with the expected energy consumption.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (7)
1. An energy efficiency coupling optimization method based on a take-off and taxi phase of an electric aircraft on water is characterized by comprising the following steps: the structure of an aircraft electrodynamic system is optimized by solving the optimal pitch angle of the propeller;
wherein said solving for the optimal pitch angle of the propeller comprises: firstly, establishing an energy consumption equation of an aircraft electrodynamic system for completing one take-off and taxi task of the aircraft; and secondly, establishing an optimization objective function of the electrodynamic force system based on the energy consumption equation.
2. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 1, wherein,
the energy consumption requirements of the aircraft electrodynamic system for completing the one-time take-off and taxi task in four different stages of a sailing stage, a transitional taxi stage, a high-speed taxi stage and a flying and leaving water stage can be expressed as follows:
wherein: e (E) g_x And W is p_x Respectively the energy consumption and the power requirement of an airplane electrodynamic system of different stages of the airplane in the process of taking off and taxiing, eta p_x 、η m_x And eta c_x The system efficiency of the propeller, the motor and the controller at different stages of the aircraft in the take-off and taxiing process is respectively; wherein the sailing stage, the transitional sliding stage, the high-speed sliding stageThe flying off-water stage is a taxiing stage of the aircraft, which is determined according to the pitch angle of the aircraft;
the optimization objective function of the electrodynamic system is as follows:
wherein: e (E) min For the minimum energy consumption of the electric power system when the aircraft completes one take-off and taxiing task, E g The total energy consumption required by the aircraft to complete one take-off taxi task.
3. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 2, wherein,
hydrodynamic resistance T of the sailing stage w From viscous drag R and wave-making drag R W Two parts, wherein the viscous resistance comprises friction resistance and shape resistance;
defining B as the width of the pontoon, and determining according to the parameters of the seaplane; by N p The number of pontoons is R e Is Reynolds number, v w For the navigational speed of the aircraft to water, the navigational speed of the aircraft is approximate to that of the water area with low static water or water flow speed, and the viscosity coefficient of the water is mu w ＝1.19*10 -6 m 2 /s，ρ w ＝997kg/m 3 Is the density of water, R e Can be expressed as:
coefficient of friction C for water f The calculation can be performed by adopting the formula of the Planta-Xu Liting:
the viscous drag R can then be calculated using the following formula:
defining coefficient K according to formula of wave making resistance calculation 0 And note gravitational acceleration g=9.8 m/s 2 Then:
building a coordinate system for the pontoon, wherein xi= (x, y, z) is the coordinates of a source point on the pontoon surface; the potential function of a source sink can be expressed as:
wherein S is the wet surface area of the pontoon under the still water, sigma is the source potential intensity distributed on the pontoon surface, c w Is the intersection of the water surface and the pontoon surface, cos (x, n) is the cosine of the angle between the pontoon surface normal and the x-axis, dw=dssin (y, n), where ds is the infinitesimal on the water line, where f x G is a green function and is a pontoon surface equation;
defining alpha as a mathematical intermediate variable, and physically representing an included angle between the travelling direction of the primitive wave and the travelling direction of the pontoon, wherein the calculation method of the wave-making resistance is as follows:
wherein S is the wet surface area of the pontoon under the still water, H 1 P is the surface pressure distribution of the pontoon, i is an imaginary unit;
from viscous drag R and wave-making drag R w Can obtain the sailing water resistance T w_1 Is that
T w_1 ＝R+R w
The thrust required to be output by the propeller can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
Wherein T is p_1 Outputting thrust for the propeller; w (W) p_1 Is the propeller power demand; r is R p Is the radius of the propeller; c (C) T The thrust coefficient of the propeller is characterized by the influence of factors such as pitch angle, wing profile, number of blades and the like on the thrust of the propeller, beta is the power coefficient of the propeller, and the beta value depends on the pitch angle, the wing profile, the number of blades and the like; c of propeller under fixed pitch angle T And the variation characteristic of beta along with the rotating speed of the propeller can be determined by a propeller wind tunnel test; ρ is air density, which can be approximately 1.29kg/m due to the limited low-altitude flight of the electric water aircraft below 3000m 3 ；n p Solving hidden functions according to the two formulas to obtain the output power of the propeller for the rotating speed of the propeller;
the total energy consumption of an aircraft during the voyage phase can be expressed as:
wherein E is g_1 T is the total energy consumption in the sailing phase g_1 For the time of sailing phase, W p_1 Power required for aircraft operation during sailing phase, where η m_1 、η c_1 And eta p_1 The efficiency of the motor, the controller and the propeller of the aircraft in the sailing stage can be obtained through the test flight data of the aircraft in the sailing stage.
4. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 2, wherein,
hydrodynamic drag T in the overrun phase w_2 From viscous drag R and wave-making drag R W Two parts, wherein the viscous drag includes frictional drag and shape drag;
coefficient of friction C for water f The mulberry equation is used at this stage to calculate:
from viscous drag R and wave-making drag R W Water resistance T for sailing w_2
T w_2 ＝R+R w
Assuming that the acceleration of the aircraft during the over taxiing phase is a 2 The required output thrust of the propeller can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as:
the total energy consumption of an aircraft during the over taxiing phase can be expressed as:
wherein E is g_2 To total energy consumption in the excessive coasting phase, t g_2 For the time of the excessive coasting period, W p_2 Power required for aircraft operation during excessive taxiing phase, where η m_2 、η c_2 And eta p_2 The efficiency of the motor, the controller and the propeller of the aircraft in the excessive taxiing stage can be obtained through test flight data of the aircraft in the excessive taxiing stage.
5. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 2, wherein,
during the high speed slip phase T D Aerodynamic drag for an aircraft can be expressed as:
wherein S is the area of the wing; c (C) D Is the aerodynamic drag coefficient; m is Mach number, the ratio of aircraft speed to sound velocity; m is M l Mach number for incoming flow, i.e., mach number of far-field gas; m is M ln For local mach number, γ is the gas specific heat ratio, γ=1.4 for air;
carrying out stress analysis on the aircraft, wherein θ is the pitch angle in the take-off and taxiing stage;the included angle between the thrust line of the electrodynamic system and the lower construction line of the aircraft can be approximately determined after the aircraft is shaped; m is the aircraft take-off quality; v is the taxiing speed of the aircraft in the horizontal direction; v fl Is the flying speed of the airplane in the axial direction, which is approximately equal to the advancing speed of the propeller, t 2 A is the time of ending the last stage 3 Acceleration during the high-speed coasting phase; r is taken s The total resistance of the aircraft in the high-speed sliding stage is received;
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
The energy consumption of an aircraft in the high speed glide phase can be expressed as:
wherein E is g_3 For total energy consumption during the high-speed coasting phase, t g_3 For the time of the high-speed coasting phase, W p_3 Power required for aircraft operation during high speed taxiing phase, where η m_3 、η c_3 And eta p_3 The efficiency of the motor, the controller and the propeller of the aircraft in the high-speed sliding stage can be obtained through test flight data of the aircraft in the stage.
6. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 2, wherein,
the hydrodynamic resistance of the floating water-leaving stage according to the Froude formula can be expressed as:
wherein l b Is the pontoon length, t w Is the water temperature;
the aerodynamic drag calculation can be expressed as:
according to the phyllin theory, the thrust and power requirements of the propeller output can be expressed as
The total energy consumption of the electric aircraft in the flying water-leaving stage can be expressed as follows:
wherein E is g_4 To the total energy consumption of the water-leaving stage of the fly, t g_4 For the time of the water-leaving stage of flying, w p_4 The power required for the operation of the aircraft in the fly-away phase, where eta m_4 、η c_4 And eta p_4 The efficiency of the motor, the controller and the propeller of the aircraft in the stage of flying and leaving water can be obtained through the test flight data of the aircraft in the stage.
7. The energy efficiency coupling optimization method based on the take-off and taxi phase of the electric aircraft on water according to claim 1, wherein the solving the optimal pitch angle of the propeller specifically comprises:
step one, assuming that the minimum pitch angle of the propeller is alpha min The maximum pitch angle is alpha max The calculated step length of the pitch angle is delta alpha, and delta alpha is less than or equal to alpha min/20;
step two, assume n= [ (α) max -α min )/Δα]Rounding up, taking n=1, pitch angle α of propeller 1 ＝α min Calculating the energy consumption required by the electric power system to complete one take-off and taxi task;
step three, taking n=n+1, and the pitch angle alpha of the propeller n ＝α n-1 +delta alpha, calculating energy consumption E required by electric power system to complete one take-off and taxi task g [n]；
Step four, judging E s [n-1]≤E s [n]Whether or not it is true, if so, E min ＝E g [n-1] The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, E min ＝E g [n] ；
Step five, judging alpha n ≤α max If yes, returning to the third step, and repeatingCalculating newly; otherwise return E min ，E min The minimum energy consumption of the aircraft for completing one take-off and taxi task is the propeller pitch angle alpha which is the minimum energy consumption of the aircraft in the take-off and taxi process, and the optimal pitch angle is obtained.
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