Aviation dynamic differential pressure propeller

Abstract

The utility model relates to an aviation dynamic differential pressure propeller. The airfoil profile of the aviation dynamic differential pressure propeller comprises an upper airfoil surface and a lower airfoil surface, the section lines of the airfoils are all composed of curves of a monotonically decreasing function from the front edge to the rear edge. The structure is simple, and when the lower wing surface does work on windward airflow, the flow speed is reduced, the static pressure intensity is increased, and upward thrust is generated; the upper airfoil does not do work, airflow flows back, static pressure is reduced, upward pulling force is generated by the airfoils, so that the lift force of the upper airfoil and the lower airfoil is upward at the same time, the sum of the lift force is larger than the lift force of an existing single-face airfoil, and then the efficiency of the propeller wing is further improved by optimizing the lift-drag ratio. A front edge point is accurately positioned by adopting a wing section line rear corner, a spanwise line, a relative velocity line and a backward moving distance, a shock wave is weakened to be low-sound-velocity object surface static pressure, and the damage effect of the shock wave is avoided.

Description

Technical Field

[0001] The utility model belongs to the field of aviation manufacturing technology, and relates to propellers for water, land and air, such as fixed-wing aircraft propellers, helicopter propellers, helicopter tail rotors, vertical take-off and landing aircraft propellers, unmanned aircraft propellers, flying car propellers, propeller fan aircraft propellers, tilt-axis aircraft propellers, seaplane propellers, ground effect aircraft propellers, ground effect wing ship propellers, hovercraft propellers, turbofan aircraft outer duct propellers, turboprop aircraft propellers, propeller aircraft, aviation turbofan engine outer duct propellers, aviation propeller engine propellers and aviation ducted propellers, etc. Background Art

[0002] Existing propellers on the water, land, and aviation all play an axial flow role in pushing the airflow, pushing the airflow backward along the axial direction to generate forward thrust. The plane expansion diagram of its airfoil is the same as the airfoil of a fixed-wing aircraft wing. The lower surface of the airfoil is flat, and the upper wing is curved upward. At a zero-degree elevation angle, lift is provided by the principle of velocity difference lift. The upper wing surface has a fast flow rate, and the static pressure decreases, forming a unilateral lift force. In addition, when the lower wing has an elevation angle, the flow rate slows down, the static pressure increases, and the airflow generates thrust on the wing surface in an upward direction. If the forces of the upper and lower wing surfaces can be superimposed and manifested at the same time, the airfoil efficiency will be improved.

[0003] In the Chinese patent "202121320870.9 A ship dynamic pressure difference propeller", the principle of dynamic pressure difference lift of incompressible water fluid is applied to achieve an airfoil that can generate lift on both the upper and lower wing surfaces at the same time, and the efficiency is significantly improved. Therefore, it is promoted and applied to compressible air fluids, so that the aviation propeller airfoil also has a double-sided lift surface at the same time, which can also improve its efficiency. Utility Model Content

[0004] The utility model aims to provide a double-sided lift airfoil capable of improving aviation air propulsion efficiency and an aviation dynamic pressure difference propeller to solve the above-mentioned problems.

[0005] In order to achieve the above object, the technical solution of the utility model is implemented as follows:

[0006] An aviation dynamic pressure difference propeller, whose cross-sectional development diagram includes an upper wing surface and a lower wing surface, is characterized in that the cross-sectional lines of the upper wing surface and the lower wing surface are both curved surfaces composed of monotonically descending curves from the leading edge to the trailing edge.

[0007] The main wing surface of the upper wing is a descending surface, and the surface is composed of a monotonically descending function. That is, from the leading edge to the trailing edge, the height of the vertical section of the surface decreases gradually, and generally there is no inflection point.

[0008] The main wing surface of the lower wing is a descending surface, and the surface is composed of a monotonically descending function. That is, from the leading edge to the trailing edge, the height of the vertical section of the surface decreases gradually, and generally there is no inflection point.

[0009] At near-sonic and supersonic speeds, the leading edge of the upper wing and the leading edge of the lower wing directly intersect.

[0010] At near-sonic and supersonic speeds, the rearward turning angle of the leading edge point of the lower wing section line is equal to or greater than the required normal angle of the leading edge point.

[0011] At near-sonic and supersonic speeds, the section line of the lower wing surface is the rearward turning angle from the leading edge to the trailing edge, and the rearward turning angle of the latter point is equal to or greater than the rearward turning angle of the former point.

[0012] At near-sonic and supersonic speeds, the back-turn angle of a spanwise line point is equal to or greater than the required normal angle of the point.

[0013] At near-sonic and supersonic speeds, the position of the leading edge point of the wing section line is determined by the relative velocity direction line and the backward distance value.

[0014] Increasing the normal angle of the wing section can improve the lift-to-drag ratio.

[0015] The zero-degree chord line of the dynamic pressure difference wing airfoil of a fixed-wing aircraft is collinear with the relative velocity direction line.

[0016] Compared with the prior art, the advantages of the embodiments of the utility model are: the utility model has a simple structure, and when the lower wing does work on the windward airflow, the flow rate slows down, the static pressure increases, and the wing surface generates an upward thrust; the airflow on the upper wing surface flows back, the static pressure decreases, and the wing surface generates an upward pull, thereby simultaneously forming the upper and lower wing surface lifts that are consistent and upward, and the sum of the two lifts is greater than the existing single-sided airfoil lift. After optimizing the lift-to-drag ratio, the propeller efficiency is further improved. When the airflow is near the speed of sound and supersonic speed, the rear turning angle of the wing section is used, and the leading edge point is accurately located using the relative velocity line and the backward displacement distance of the spanwise line, weakening the shock wave to the static pressure of the low-speed object surface, thereby avoiding the destructive effect of the shock wave. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of horizontal non-thick pipe

[0018] Figure 2 Schematic diagram of horizontal straight uniform flow

[0019] Figure 3 Schematic diagram of static pressure calculation on the frontal surface

[0020] Figure 4 Schematic diagram of static pressure calculation on the back flow surface

[0021] Figure 5 Schematic diagram of propeller horizontal position

[0022] Figure 6 A top view of the velocity triangle at point A

[0023] Figure 7 Projection diagram of the distance M moves backward

[0024] Figure 8 Schematic diagram of the setback distance in the top view

[0025] Fig. 9 Schematic diagram of fixed-wing aircraft airfoil cross section

[0026] Fig.10 Horizontally symmetrical diagram of the left part

[0027] Fig.11 Transition diagram after the horizontal length is doubled

[0028] Fig.12 Screenshot of the new airfoil at 75% length

[0029] Fig.13 Schematic diagram after optimization and improvement DETAILED DESCRIPTION

[0030] The following will clearly and completely describe the technical solutions of the utility model embodiments in conjunction with the drawings. Obviously, the described embodiments are only part of the embodiments of the utility model, not all of the embodiments. Based on the embodiments in the utility model, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the utility model.

[0031] Example

[0032] 1. Principle of propeller lift due to dynamic pressure difference in aviation

[0033] The lift principle, main reasoning and conclusion of aviation dynamic pressure difference propeller can directly apply the lift principle, main reasoning and conclusion of water fluid dynamic pressure difference given in the Chinese patent "202121320870.9 A kind of ship dynamic pressure difference propeller". Because water and air are both incompressible fluids (when the speed is lower than 0.2 times the speed of sound, air can be considered as an incompressible gas), the water parameters can be replaced with incompressible air parameters, and the same reasoning can be applied to the concept. When the air velocity is equal to or greater than 0.2 times the speed of sound, the above formulas, reasoning and conclusions can be expanded using compressible fluid, perfect gas (air is considered to be a perfect gas), isentropic and high-speed one-dimensional steady flow, and can be applied to the dynamic pressure difference wing airfoil of low-sonic fixed-wing aircraft, and then to the dynamic pressure difference propeller airfoil of aviation; at near-sonic and supersonic speeds, combined with the influence of shock waves, the leading edge point is located using the rear turning angle of the lower wing section and the spanwise line relative velocity line and the backward displacement distance, which can weaken the strong static pressure of the object surface shock wave to the static pressure of the low-sonic speed, thereby eliminating the destructive effect of the shock wave.

[0034] 2. The propeller moves in the air flow field and does work

[0035] Basic formula for work in pipeline fluid dynamics

[0036] Assuming that the ideal irrotational flow field is a constant flow, the mass force is only gravity, the flow is along the element flow (streamline), and the gas flow is incompressible, the integral of the differential equation of motion along the streamline, plus the input mechanical energy, such as the fan, etc., the total flow Bernoulli equation is obtained as:

[0037]

[0038] For a straight, smooth, round pipe without thickness, placed horizontally in the gas flow field, the position term can be ignored, and we get:

[0039]

[0040] In the formula: z is the height from a certain reference surface; u is the flow velocity; p is the static pressure; g is the acceleration due to gravity; ρ is the density, subscript 1 is the initial section, 2 is the final section, H m is the mechanical energy obtained by unit weight of fluid through fluid machinery, is the external energy, and α is the kinetic energy correction coefficient, where 1 is taken.

[0041] Multiply both sides of the equation by ρg, and let ρg H m =H, H is the input mechanical energy, called external pressure, and after sorting, we get:

[0042]

[0043] The parameters in (1) and (2) are the centroid parameter values. For a circular pipe, the centerline of the pipe is the centroid. The above formula is used for incompressible air fluids with a velocity lower than 0.2 times the speed of sound. It can be used for aviation fixed-wing airfoils and aviation propeller airfoils. Air parameters should be substituted when applying.

[0044] Assume that a straight pipe with limited length, smooth, round shape and small radius R is placed horizontally in the air flow field. The pipe is stationary, the coordinate axis is fixed on it, and the horizontal axis coincides with the center line of the pipe. B is the inlet end, C is the external machine, A is the outlet end, and the air flow in the pipe flows from right to left. The schematic diagram of the horizontal non-thick pipe is as follows Figure 1 shown.

[0045] When the air velocity in the flow field is zero and the steady velocity in the pipe is u, any point in the inlet pipe BC is selected as section 1, and any point in the outlet pipe AC is selected as section 2.

[0046] At section 1, there is a velocity u, flowing from right to left. Its kinetic energy is converted from the static energy of the flow field (also called background static energy). Therefore, the static energy of pipe BC is twice as low as the background static energy. At section 2, there is a velocity u, but the air needs to be discharged to the outlet. Therefore, the static energy must be equal to or greater than the background static energy to discharge the gas smoothly. Here, it is a constant velocity and is equal to. Substituting into formula (1), the work done is:

[0047]

[0048]

[0049]

[0050]

[0051] This means that as long as the air velocity in the tube is greater than zero, the external machine will always do work. 背 is the static pressure intensity of the background flow field.

[0052] If we imagine the flow field as a pipe of infinite diameter with a horizontal straight pipe of finite length and small diameter inside, then, Figure 1 The small tube and the large tube form a fluid circuit. As long as the airflow passes through the external mechanical part C, the energy will be increased.

[0053] In this way, the entire flow field consists of three parts: outlet pipe, large pipe (background flow field), and inlet pipe. The flow direction is: the inlet pipe section sucks the flow field fluid from the inlet end, and after the energy is increased by external force, it is discharged into the outlet pipe section, flows into the background flow field through the outlet end, and then flows to the inlet end through the background flow field.

[0054] The energy of the entire flow field is divided into two areas, among which the energy in the outlet pipe AC is one area, which has twice the kinetic energy than other areas.

[0055] If formula (2) is used and the effect of velocity is taken into account, the static pressure of the entire flow field can be divided into three regions: the outlet section has the highest static pressure (when the fluid is set to a stationary coordinate, the velocity is the dynamic pressure, which can be converted into static pressure), the background flow field has the second highest static pressure, and the inlet section has the lowest static pressure, with the difference being one times the dynamic pressure.

[0056] Use a non-thick rigid flat sheet with a radius equal to the inner radius R of the pipe, perpendicular to the paper surface, and drive the airflow to move horizontally to the left along the center line of the pipe at a constant speed u, replacing the external mechanical work. The work can be calculated using the pipe formula (1). At this time, the airflow on the right surface of the sheet, due to the leftward movement of the sheet, the inlet pipe section becomes longer, and the incompressible airflow has not yet flowed in from the inlet end. The airflow and the sheet are separated, and the separation speed is u. This space is a vacuum. At the inlet end, the airflow is the static pressure of the flow field, and the right side of the sheet is a vacuum. Under the action of the static pressure difference between the two, the flow field airflow flows into the inlet pipe section to fill the vacuum area. When the flow speed reaches u, it is equal to the separation speed of the sheet, reaching flow equilibrium, and the vacuum disappears. From formula (2), it is known that the static pressure of the inlet pipe section is twice the dynamic pressure of the static pressure of the flow field.

[0057] When the pipe is extremely short, formula (1) still applies; when it tends to be infinitely short, it still applies. When it is equal to zero, it is equivalent to the individual motion of the sheet without the pipe section. For the sheet with and without the pipe, assume that both are doing the same horizontal motion from right to left, with a speed of u. The static pressure of the flow field on the left side of the two sheets is the same, which is equal to the static pressure of the background flow field. Due to the movement of the sheet, the air is separated from the sheet on the back of the right side of the two sheets, and a vacuum is generated on the back side of the sheet. The gas on the right side of the sheet is the static pressure of the background flow field. The air between the static pressure of the flow field and the vacuum moves to the vacuum area under the action of the static pressure of the flow field. When the flow balance is reached, the vacuum area disappears, the flow velocity is u, and the static pressure on the right side of the sheet is the dynamic pressure of the static pressure of the flow field dropping by one times. Therefore, the two sheets are subjected to the same force, and the work done by both is equal. The amount of work done can be calculated using formula (1) with pipes. The motion of the sheet without pipes can be regarded as the motion of the sheet with pipes. The two sheets do the same horizontal motion in the flow field and the amount of work done is equal.

[0058] When a non-thick rigid flat sheet moves alone in a static flow field, the gas energy in front of it is higher and the static pressure on the back is the lowest.

[0059] The aircraft propeller moves in the air fluid and can be considered as a rigid body. Its surface can be divided into countless small pieces. Formula (1) can be applied to each small piece to calculate the micro work. Finally, by summing them up, we can get the work done by the propeller.

[0060] In the flow calculation of pipeline fluid, when the air velocity is at an angle with the centerline of the pipeline, the velocity needs to be decomposed into two components, one parallel to the centerline and the other perpendicular to it. The parallel component forms the pipeline flow and constitutes the work flow, while the perpendicular flow does not do work. Therefore, we only need to find the velocity component parallel to the centerline and substitute it into the formula for calculation.

[0061] After changing the conditions of formula (1) to compressible gas, adding perfect gas, isentropic, and one-dimensional high-speed steady flow, the formula for pipeline work is:

[0062]

[0063] Where γ is the specific heat ratio, subscripts 1 and 2 are the corresponding parameters of pipe sections 1 and 2 respectively, and the usage is the same as formula (1).

[0064] Similarly, when an aircraft propeller moves in an air flow field, its surface can be divided into countless small pieces. Formula (3) can be applied to each small piece to calculate the micro-work (quantity). Finally, by summing them up, we can get the work done by the propeller.

[0065] 3. Static pressure strength of aviation propeller airfoil section

[0066] It is divided into incompressible airfoil section static pressure and compressible airfoil section static pressure.

[0067] The incompressible propeller airfoil section is the wing airfoil section of a fixed-wing aircraft. Under incompressibility, they are the same as the airfoil section of the lower wing of a ship, so the fluid formula and results of the underwater wing can be directly applied, but the parameters are air parameters. The compressible one needs to use the incompressible theory extension. At low speeds, there is no need to calculate the rear turning angle and the backward displacement; but at near-sonic and supersonic speeds, it is necessary to calculate the rear turning angle of the lower wing section, the spanwise relative velocity angle and the backward displacement to determine the position of the wing leading edge point, so as to weaken the shock wave.

[0068] Incompressible airfoil section static pressure strength.

[0069] There is no left and right (front and back) static pressure difference for a thick rigid flat sheet.

[0070] The coordinate origin is fixed to the center point of the sheet, the X axis is placed horizontally, the direction is right, and the Y axis is upward. The air flow in the flow field becomes a horizontal straight uniform flow, moving from left to right. Figure 2 shown.

[0071] According to the incompressible Bernoulli level formula in the flow field:

[0072]

[0073] Find the static pressure p on the left side of the film 片左 Select the far left end of the flow field as section 1, the left side of the sheet as section 2, and substitute into formula (4) to obtain:

[0074]

[0075]

[0076] That is, the left side of the film converts the dynamic pressure of the gas at the far end into static pressure. The static pressure on the left side of the film is p 片左 The dynamic pressure is twice the static pressure of the flow field.

[0077] Find the static pressure p on the right side of the plate片右 The air in the flow field moves horizontally to the right at a speed of u, and the gas separates from the right side of the sheet at a speed of u. The separation area is a vacuum. Under the action of the static pressure difference between the static pressure of the flow field and the vacuum, the air quickly moves along the horizontal line to the right back side of the sheet. When dynamic equilibrium is reached, the speed of the air moving to the back side is u, and the static pressure on the back side of the sheet is the dynamic pressure of the static pressure of the flow field down by one times, that is:

[0078]

[0079]

[0080] The difference in static pressure between the left and right sides of the sheet is 2 times the dynamic pressure:

[0081] p 片左右差 =p 片左 -p 片右 =ρu 2 .

[0082] The airfoil section of an aviation propeller is a closed smooth transition curve, which we represent with a circular curve. By finding the static pressure at any point on the curve, we can apply it to find the static pressure at any point in the wing section. When calculating the area, take 1 unit length in the span direction.

[0083] Assume that the section of the wing cross-section diagram is a circular curve with a radius of R. The circular curve is parallel to the surface. The infinitely far horizontal parallel air flow flows from left to right at a velocity u. The origin of the coordinate axis is fixed at the same position as the center of the circle. The horizontal axis X is placed horizontally and points to the right. The vertical axis Y is vertically upward. The normal direction of the curve is positive within the static pressure of the air. Point A is the intersection of the straight uniform airflow and the circumference. Line B is the normal to point A. Line C is the tangent to point A. α is the angle between the straight uniform airflow and the normal. According to the meaning of formulas (2) and (4), on the frontal surface, in the second and third quadrants, the fluid collides head-on, which is the normal component. The normal velocity becomes zero, and the dynamic pressure will be completely converted into static pressure. The direction of the increased static pressure points to the center of the circle. The tangential component has no collision and remains unchanged. The schematic diagram of the static pressure calculation on the frontal surface is as follows: Figure 3 shown.

[0084] According to the meaning of formulas (2) and (4), the normal flow velocity = u × cosα, and the sum of the background static pressure and the added static pressure is the static pressure value at point A on the frontal surface:

[0085]

[0086] The second and third quadrants are symmetrical figures with the horizontal axis. The static pressure values ​​at the symmetrical points are equal in magnitude and along the inner normal direction. The static pressure formed is thrust, which is equal in magnitude and also along the inner normal direction. The static pressure component formed in the horizontal direction is resistance, which is equal in magnitude and in the same direction. The static pressure component formed in the vertical direction is lift, which is equal in magnitude. In the second quadrant, the component is negative lift, and in the third quadrant, it is positive lift.

[0087] The back flow surface is composed of the first and fourth quadrant curves of the circular curve. Point A is the intersection of the reverse straight uniform airflow (the velocity is equal to that of the straight uniform airflow, but the direction is opposite) and the circumference. Line B is the normal line of point A, line C is the tangent line of point A, and α is the angle between the reverse straight uniform airflow line and the normal line. Figure 4 shown.

[0088] According to the meaning of formulas (2) and (4), the normal flow velocity = u × cosα, and the normal flow velocity on the backflow surface is converted from the static pressure of the background flow field, which reduces the static pressure. The difference between the background static pressure and the newly added static pressure is the static pressure value of point A on the backflow surface:

[0089]

[0090] The direction of the static pressure is the same as the inner normal, pointing toward the center of the circle, but it is decreasing.

[0091] The first and fourth quadrants are symmetrical figures with the horizontal axis. The static pressure values ​​at the symmetrical points are equal in magnitude and along the inner normal direction. The static pressure formed is a pulling force (suction force), which is equal in magnitude and along the outer normal direction. The static pressure component formed in the horizontal direction is a drag force, which is equal in magnitude and in the same direction. The static pressure component formed in the vertical direction is a pulling force, which is equal in magnitude. In the first quadrant, the component is a positive lift, and in the fourth quadrant, it is a negative lift.

[0092] In summary, the static pressure value of a point A on the wing section line is:

[0093]

[0094] The plus sign in the formula is the upstream surface, and the minus sign is the downstream surface. The formula shows that when the upper wing surface is used, the first quadrant intercept should be used, and the intercept is a monotonically decreasing function curve without an inflection point; when the lower wing surface is used, the third quadrant intercept should be used, and the intercept is a monotonically decreasing function curve without an inflection point, so as to form a consistent double-sided positive lift airfoil, that is, a dynamic pressure difference airfoil.

[0095] For the convenience of discussion, we limit the lift-to-drag ratio of a point on the wing section line to the first and third quadrants, and consider it as the ratio of the absolute value of the lift increased by the dynamic pressure at that point to the absolute value of the drag increased by the dynamic pressure. Then the static pressure increment in formula (5) is multiplied by the static pressure of the smallest unit area at this point, and then projected in the vertical and horizontal directions respectively, and the ratio is calculated, which is the lift-to-drag ratio of the point:

[0096]

[0097] It means that the larger the angle, the higher the lift-to-drag ratio. Under the lift conditions, the angle should be increased as much as possible to improve the efficiency of the wing; the larger the angle, the larger the rear turning angle, the lower the static pressure on the surface, and the more it can avoid shock wave damage. The micro-segment of the intercept of a point can be considered as a straight line. If the straight line is extended only in the horizontal direction, the normal angle becomes larger, the tangent value increases, and the lift-to-drag ratio increases; similarly, if it is extended in the vertical direction, the lift-to-drag ratio decreases; extending the intercept in the horizontal direction to improve the lift-to-drag ratio is an effective method.

[0098] The above is the reasoning and conclusion of the lift principle of dynamic pressure difference in incompressible fluid when the air flow is lower than 0.2 times the speed of sound.

[0099] Compressible airfoil section static pressure strength.

[0100] In the flow field, the parameter relationship between sections 1 and 2 of compressible, perfect gas, isentropic, one-dimensional high-speed steady flow is:

[0101]

[0102]

[0103] The static pressure value p on the left side of the plate 片左 When the airflow flows from the far left end to the left side of the sheet, it is an isentropic compression process. The far left end of the flow field is selected as section 1, and the parameters are flow field parameters; the left side of the sheet is section 2, and the velocity parameter is zero. Substituting into formula (6) yields:

[0104]

[0105]

[0106] When the airflow at point A of the tangent line has a normal angle, the static pressure intensity p α Substituting the normal velocity u cosα, we get:

[0107]

[0108] The static pressure value p on the right side of the plate 片右When the gas on the right side of the sheet moves to the right along with the velocity of the flow field, it separates from the sheet and a vacuum space appears. Under the action of these two forces, the gas between the static pressure of the flow field and the vacuum fills the vacuum interval in an isentropic expansion process. When equilibrium is reached, formula (6) gives:

[0109]

[0110] When the airflow at point A of the tangent line has a normal angle, the static pressure intensity p α Substituting the normal velocity u cosα, we get:

[0111]

[0112] Formula (7) is used for the upstream surface, and formula (8) is used for the downstream surface.

[0113] The formula shows that the upper wing surface should use the first quadrant section line, and the section line height decreases monotonically from the leading edge to the trailing edge without an inflection point; the lower wing surface should use the third quadrant section line, and the section line height decreases monotonically from the leading edge to the trailing edge without an inflection point; only in this way can a consistent positive lift biface be formed at the same time to form a dynamic pressure difference airfoil.

[0114] At low sound speeds, the above formula can complete the lift design and improvement of the cross-section.

[0115] However, at near-sonic and supersonic speeds, the influence of shock waves must also be considered. Shock waves can reduce the strong surface static pressure of the positive shock wave to the low-speed static pressure of the surface by making an angle with the normal of the oncoming surface.

[0116] When the normal angle rotates from 0 degrees to α, its tangent also rotates α accordingly, which is called the tangent back rotation angle, or back rotation angle for short. The back means rotation along the velocity direction; the object plane back rotation angle is when the normal angle rotates from 0 degrees to α, its object plane also rotates α accordingly, which is called the object plane back rotation angle here. The angle values ​​of the back rotation angle, object plane back rotation angle, and normal angle are equal. At near-sonic and supersonic speeds, increasing the back rotation angle will reduce the normal speed, work done, and the static pressure on the object surface. It is used for the tangent back rotation angle and the spanwise back rotation angle to weaken the point that exceeds the static pressure to a point that is equal to or less than the static pressure required for low sound speed.

[0117] The straight uniform air flow velocity u at point A is the relative speed of the velocity triangle of the finger point in the propeller. Within the range of 5 times supersonic speed, the calculation result of the above formula is generally considered to be within an acceptable error range.

[0118] At near-sonic and supersonic speeds, shock waves will be generated on the windward surface, and the normal angle of the windward surface needs to be calculated to reduce the windward speed to the required normal speed and the required surface static pressure. There is no shock wave on the leeward side, so there is no need to calculate it. From formula (7), the normal angle of the windward surface is:

[0119] We limit the range of α to 0 to 90 degrees. The larger the value, the smaller the normal velocity and the lower the static pressure on the surface. Based on practice, we often recommend the highest specified value of the low-sonic velocity value (the highest specified value of the low-sonic velocity value can be used to calculate the highest specified value of the static pressure on the surface at a point). If it is equal to or less than this value, it is considered to have reached the low-sonic surface static pressure value, eliminating the adverse effects of the shock wave and will not damage the body.

[0120] At near-sonic and supersonic speeds, the relative speed of the leading edge of the wing section will increase with the increase of the propeller radius, and the angle of the leading edge will also increase. Substitute the highest low-sonic speed specified value and the cosine zero value into formula (7) to calculate the highest low-sonic specified static pressure value, and then substitute this static pressure value and the relative speed value of the point into formula (9) to calculate α i When the rear turning angle of each point is equal to or greater than this angle, the normal velocity and static pressure value of each point will not be higher than that of the leading edge point; if the rear turning angle of the rear point is equal to or greater than that of the front point, no secondary shock wave will be generated. In this way, the static pressure value of each point on the wing section line will not exceed the maximum specified value of the static pressure value of the low-sonic surface.

[0121] The spanwise line is a line perpendicular to the relative velocity. When it is near the speed of sound and supersonic, it will also encounter the strong static pressure generated by the normal shock wave similar to the cross section line. It is necessary to reduce the static pressure value of the object surface. Using the same derivation process of the wing cross section line to obtain the included angle, the same spanwise line angle formula (9) can be derived.

[0122] As the radius increases, the spanwise angle also increases, and the angle must be calculated at each point. The spanwise angle is substituted into formula (7) with the highest low-sonic speed specified value and the cosine zero value. After calculating the highest low-sonic speed specified static pressure value, this static pressure value and the relative speed value of the point are substituted into formula (9) to calculate α i If the angle behind the spanwise line is equal to or greater than the included angle, the static pressure value of the object surface at this point will not exceed the maximum specified value of the static pressure value of the object surface at low sound speed.

[0123] Different airfoils have different maximum speed limits for low-speed sound. Here we take a metal wing as an example. The static pressure value at the wing point is not higher than 0.95 (to 0.97, here we take 0.95) times the speed of sound u 0.95 The static pressure value p 0.95 , we can convert u 0.95Substitute the cosine value equal to 1 into formula (7) to find the p of the point 0.95 ; Then the radius r i The real relative velocity u of the leading edge point at i and p 0.95 Substitute into formula (9) to obtain the normal angle α i , the static pressure value of this point at this angle is equal to p 0.95 , when the angle is greater than this, the static pressure value is less than p 0.95 If applied to all the propeller sections and span lines, the propeller surface will reach p 0.95 The requirements are met, achieving the purpose of weakening the shock wave to the static pressure strength of the low-speed sound object surface.

[0124] The propeller should use the maximum outer diameter R2 to calculate the relative speed value. If the calculated speed is equal to or less than u 0.95 , it is considered to be a low-sonic propeller; if it is greater than u 0.95 , considering it to be a near-sonic and supersonic propeller, it is necessary to calculate u 0.95 The radius r0 when the sound velocity is less than r0 is treated as low sound velocity; the point equal to r0 is marked as A0, and the points from A1 to A n The point is used to calculate the rear turning angle of the intercept line of near-sonic speed and supersonic speed, and the rear turning angle and rearward displacement value of the spanwise line.

[0125] The backward distance value is the straight line length between the leading edge point position of the airfoil and the initial position. When the normal angle of a certain point on the span line rotates from 0 degrees to an angle of α, the intersection with the relative velocity direction line also moves a straight line distance accordingly. The distance (value) of this straight line movement is called the backward distance (value), or simply the backward (value). Therefore, the initial intersection point of the backward turning angle of 0 degrees is the initial point of the backward distance, and the final intersection point is the end point of the backward distance. The straight line distance between the two points is the backward distance.

[0126] The propeller pushes the airflow backwards to form an axial flow, which plays a role in generating axial forward thrust. It can be imagined that the propeller shaft is placed in a horizontal position and rotates in place. The airflow flows in from the front of the shaft, passes through the blades, and then flows to the rear of the shaft. The coordinate axis is horizontally overlapped with the rotation axis. The coordinate origin is represented by O as the original position of the propeller. The Z axis is to the left, the Y axis is vertical, and the X axis is horizontal and vertical to us. r is an arbitrary radius, A represents the leading edge point of the wing, and all leading edge points are on the spanwise (radial) line of the origin when the speed is zero. We assume that the leading edge point of the blade under study is exactly on the Y axis, and R2 represents the maximum radius of the blade. At near-sonic and supersonic speeds, R1 indicates the radius r0 of the starting point of the blade's rearward turning angle, and A0 indicates the leading edge point at the radius r0 (also the maximum speed limit point specified for low-sonic speed); suppose there are n equally spaced points between R1 and R2, starting from the zero mark A0, corresponding to the radius r0 (R1 equals r0); the nth mark ends, corresponding to the mark A n , radius r n (R2 is equal to r n ); the middle i-th point is punctuated by A i Points represent the corresponding radius r i ; Use A before the i point i-1 Indicates that the corresponding radius r i-1 The propeller blades rotate in the direction from the inside to the outside of the book above the shaft. The horizontal position diagram of the propeller is as follows: Figure 5 shown.

[0127] The velocity triangle of point A on the propeller is a right triangle composed of absolute velocity, involved velocity, and relative velocity, on the horizontal tangent plane of point A. Among them, the horizontal absolute airflow velocity u at point A is 气 is a right-angle side; the involved speed is u 牵 (u 牵 =2πrn s , where n s is the number of rotations per second) is the other side of the right angle; relative speed u 相 (equal to the square root of the sum of the two squares) is the hypotenuse. Figure 5 Make a top view of point A. The angle between the relative velocity and the drag velocity is β, which is called the relative velocity angle. The M direction is the projection direction perpendicular to the relative velocity. Figure 6 shown.

[0128] Make a rotating cylinder with radius r. On the 360-degree cylinder, at any angle on the generatrix, the horizontal absolute airflow velocity u at each point is 气 , the speed u 牵 , relative speed u 相The sizes are all equal, the three sides of the velocity triangles at each point are equal, the figures are also completely equal, and the velocity triangles at each point are all on the tangent plane of the point. The generatrix of each point is the tangent, which is both a line on the tangent plane and a line on the cylinder. It is the colinearity of the tangent plane and the cylinder, and the velocity triangles overlap and are shared. The generatrix on the cylindrical surface is parallel to the axis, and the angles between the relative velocity direction lines of each point and the generatrix and the axis are equal. Starting from point A (set to zero degrees), the cylindrical surface is horizontally rolled 360 degrees on the horizontal tangent plane at point A to form an unfolded diagram of the horizontal tangent plane at point A with a radius of r. The velocity triangles of each point on the unfolded plane are all imprinted from the generatrix of the cylinder, which are congruent triangles, in which the relative velocities are equal in size and in the same direction, forming a plane relative velocity straight uniform flow. If the spanwise thickness is 1 (that is, the radius increment is 1), a three-dimensional relative velocity straight uniform flow is formed. If the radius increment approaches zero, the thickness of the unfolded diagram approaches zero, and the gas parameters of the unfolded diagram will be very consistent and very accurate. If the designed plane unfolded airfoil section is rolled back from the end of the roll (360 degrees) on the unfolded plane to the starting point A (0 degrees), the plane section will be imprinted on the cylinder surface, becoming a cylinder section, plus the small thickness in the span direction, it is a small section of the propeller. The cross-sectional view of the propeller we consider here is the cross-sectional view of the propeller formed by unfolding the cylindrical surface with a radius r and a generatrix parallel to the propeller axis around the axis into a plane. We only take one propeller for discussion. The cross-section of the propeller is designed under the horizontal relative velocity straight uniform flow. The chord line is consistent with the airflow direction, and the efficiency is higher (the airflow direction is parallel to the chord line. When the lift is the same, the normal angle is larger than the non-parallel tangent angle, and the efficiency is higher); if the angle between the relative velocity direction line and the mother line is marked on the horizontal line, a line is drawn, and this line is the axial line. Then the projection of the force generated by the straight uniform flow on the airfoil cross-section on the axial line is the axial thrust; reflected on the cylindrical surface, the force of the relative velocity airflow on this cross-section is the axial thrust in the axial projection, and the axial thrusts of the two are equal. The dynamic pressure difference wing airfoil of the fixed-wing aircraft is designed in the horizontal straight uniform flow. If the horizontal straight uniform flow velocity is equal to the relative velocity, and the chord line is designed to be zero angle (the chord length of the dynamic pressure difference airfoil in this article refers to the distance between the projections of the leading and trailing edges on the chord line, and the chord line is a horizontal line), the designed airfoil is the propeller cross-section airfoil, which can be directly used as the propeller cross-section airfoil. If you need to find the axial thrust, you can mark the axial line, find the sum of the forces at each point, and then project it to get the axial thrust. Place the designed fixed-wing dynamic pressure difference wing airfoil on the horizontal tangent plane expansion diagram at point A, place the leading edge point of the wing section at point A of the propeller, and align the chord line with the relative speed direction to form a dynamic pressure difference propeller airfoil. Therefore, by directly using the plane relative speed straight uniform flow and the zero-degree chord line to design the dynamic pressure difference fixed-wing wing section diagram, you can design a well-fitting dynamic pressure difference propeller airfoil section diagram; and if it is not equal to the relative speed, it is also its airfoil, but the degree of fit is not as high.In this way, to design a dynamic pressure difference propeller airfoil, you first design the dynamic pressure difference wing airfoil of a fixed-wing aircraft, make the airfoil and the cross-sectional view in the same plane, and then place the zero-degree chord in the appropriate position of the leading edge point according to the relative velocity direction, and it becomes a dynamic pressure difference propeller airfoil.

[0129] The propeller span line, at the specified static pressure intensity p of 0.95 times the supersonic speed 0.95 When , the corresponding point is A0 (corresponding radius is R1). If the radius is increased, the leading edge point A i The relative velocity direction line and the backward distance value must be used to meet the requirement of not exceeding the static pressure intensity p 0.95 .

[0130] In A0 to A n The relative velocity angle β between points is β0 to β n ,u 牵 As the radius increases, the angle β gradually decreases, and the angle β value is between zero and 90 degrees. i Through the velocity triangle we can obtain:

[0131] tanβ=u 气 ÷u 牵

[0132] β=arctan(u 气 ÷2πr n s )………………(10)

[0133] The above formula determines the direction of the relative velocity at point A on the horizontal tangent plane. At near-sonic and supersonic speeds, starting from A1, β = β i =arctan(u 气 ÷2πr i n s ), r=r i , A uses A i Mark.

[0134] After determining the relative velocity direction, determine the i The distance that a point moves in a straight line in the direction of relative velocity. i Indicates span line A i The back angle value of the point; the tangent parallel line is A i The parallel line of the tangent line of point A i-1 intersects with A i The horizontal line intersects at point K; l i kA is the straight line segment i Distance, A i The backward distance of the point, M is the projection diagram of the backward distance, such as Figure 7 shown.

[0135] The difference in radius length Δr between adjacent leading edge points (from the current point to the previous point) is: Δr = (R2-R1) / n.

[0136] The backward displacement value of point A1 is l1=Δr×tanα1; accordingly, A i The point's backward displacement value is l i =Δr×tanα i .

[0137] Use S i Indicates A i The cumulative value of the point's backward movement, which is from l1 to l i Along β i The sum of the projections in the direction (or the relative velocity of the airflow between the points in β i The sum of the backward shift values ​​formed by the projections in the direction of Figure 5 The top view of the new coordinate system is created. The origin is still the old coordinate origin, represented by O, with the Y axis pointing upward and the X axis pointing to the right. The front edge point A overlaps with the origin and is above. Figure 8 shown.

[0138] The backward cumulative value S of the i-th point i :

[0139] S i =l1cos(β1-β i )+l2cos(β2-β i )+…+l i-1 cos(β i-1 -β i )+l i cos(β i -β i )……(11)

[0140] The above is the principle of aviation propeller lift due to dynamic pressure difference, and it is also the principle of aviation propeller lift due to dynamic pressure difference. It will be applied below.

[0141] 4. Fixed-wing aircraft dynamic pressure difference wing airfoil

[0142] In the design of the dynamic pressure difference airfoil, the relative speed is taken as a horizontal straight uniform flow, and the chord angle is zero. According to formulas (7) and (8), the first quadrant intercept is selected for the upper wing surface, and the intercept is a monotonically decreasing function curve; the third quadrant intercept is selected for the lower wing surface, and the intercept is a monotonically decreasing function curve; at low sound speed, the two are connected at the leading edge through a smooth inner arc (without shock wave influence) to form a wing, and the trailing edge is directly connected to form a wing to form a dynamic pressure difference wing; at near-sonic speed and supersonic speed, it is necessary to calculate u 0.95 The radius r0 when the sound velocity is less than r0 is treated as low sound velocity; the point equal to r0 is marked as A0, and the points from A1 to A nThe leading edge point of the lower wing is p 0.95 and the relative velocity of this point, and substitute into formula (9) to calculate the value of A1 to A n The normal angle of the point, when the rear turning angle of the leading edge point of the lower wing is equal to or greater than this angle, the lower wing and the upper wing are directly connected at each point. The rear turning angle of the section line from the leading edge point to the trailing edge point must satisfy that the rear turning angle of the latter point is equal to or greater than the rear turning angle of the former point to avoid the influence of shock waves. In this way, both the upper and lower wing surfaces will generate positive lift at the same time, and then according to the point lift-to-drag ratio, the section line with higher efficiency is selected to further improve the lift-to-drag ratio.

[0143] The current wing based on velocity difference lift principle is changed to a wing based on dynamic pressure difference

[0144] Assume that it is a fixed-wing airfoil with a straight and uniform relative velocity flow field. The upper wing surface is an upward arc, point A is the leading edge, point B is the trailing edge, the lower wing surface is horizontal, AB is the chord length, C is the highest point, D is the foot of C, and the distance between point D and point A is 25% of the length of AB. If the straight and uniform airflow flows horizontally from left to right, curve AC is the oncoming surface and curve CB is the venting surface. Therefore, the upper wing surface curve ACB should remove the oncoming surface and leave the venting surface. The schematic diagram of the cross-section of the fixed-wing aircraft airfoil is as follows: Fig. 9 shown.

[0145] Take the left part ACD and make a symmetrical image with the horizontal line as the axis of symmetry as part ADE. The lift of the two curves in the symmetrical image is equal in magnitude but opposite in direction; the horizontal drag is equal. Fig.10 shown.

[0146] Draw a graph of the ADE part, the length of AD is 25% of AB, extend the AD horizontal line twice, get the AF horizontal line, AF is 75% of AB length, through point F, draw a vertical line, take point G, and make GF equal to the length of DE. Make the AG curve of the AFG part (shown by the dotted line) have the same curve type as the AE curve. Due to the horizontal extension, the normal angle of the AG curve is larger, the tanα value is higher, and the lift-to-drag ratio is higher. The transition diagram after the horizontal length is extended by twice is as follows Fig.11 shown.

[0147] Will Fig. 9 The CB curve is used as the upper wing surface, and Fig.11 The AG curve is used as the lower wing surface, that is, point C is connected to point A, point B is connected to point G, the horizontal lengths of the two are equal, and the vertical heights are equal, forming a new dynamic pressure difference airfoil, where the solid line represents the upper wing surface, and the dotted line represents the lower wing surface. The schematic diagram of the new airfoil with a length of 75% is shown in the figure. Fig.12 shown.

[0148] The new dynamic pressure difference airfoil generates positive lift on both the upper and lower surfaces, forming a double-surface lift wing with an additional lift surface, which significantly improves the lift-to-drag ratio.

[0149] Increasing the normal angle can further improve the lift-to-drag ratio of the airfoil.

[0150] According to the point lift-to-drag ratio, we will Fig.12 The leading edge point C (A) in the figure is horizontally extended to the left by 25% of the length of AB. The upper wing section line CB (solid line) and the lower wing section line AG (dashed line) are extended according to their similar line types. The extended CB (solid line) and AG (dashed line) form a smoother and more efficient new airfoil, which further improves the lift-to-drag ratio of the airfoil. The schematic diagram after optimization and improvement is shown in the figure below. Fig.13 shown.

[0151] 5. Aviation dynamic pressure difference propeller

[0152] The above obtained fixed-wing aircraft dynamic pressure difference wing airfoil can be directly used as an aviation dynamic pressure difference propeller airfoil. The wing airfoil and the plane unfolding surface diagram of the propeller leading edge point A are in the same plane, the chord line and the relative speed are in the same line, and then the leading edge point is overlapped with point A, and then it becomes an aviation dynamic pressure difference propeller airfoil.

[0153] exist Figure 6 In the diagram, select a certain radius r of the propeller shaft and the position of the leading edge point A, and make a horizontal plane expansion diagram of point A. Fig.13 The leading edge of the airfoil coincides with point A on the plane; the angle β is calculated by formula (10) to determine the relative velocity angle β, so that the zero-degree chord line of the fixed-wing airfoil is collinear with the relative velocity motion direction line, and the airfoil also overlaps with the plane (in the same plane); this airfoil section is the required aerodynamic pressure difference propeller airfoil section. For low-sonic speeds, the preparation of an airfoil plane expansion diagram of the propeller has been completed. However, at near-sonic and supersonic speeds, it is necessary to calculate u 0.95 The radius r0 when the sound velocity is less than r0 is treated as low sound velocity; the point equal to r0 is marked as A0, and the points from A1 to A n The leading edge point of the lower wing is p 0.95 and the relative velocity of this point, and substitute into formula (9) to calculate the value of A1 to A n The normal angle of the point. When the rear turning angle of the leading edge point of the lower wing is equal to or greater than this angle, the rear turning angle of the transverse line from the leading edge point to the trailing edge point must satisfy that the rear turning angle of the latter point is equal to or greater than the rear turning angle of the former point. The spanwise line needs to calculate the relative velocity angle β according to formula (10): i , confirm that after A i The relative speed direction of the point; the backward cumulative value S is calculated according to formula (11) i , and then Fig.13 The leading edge of the airfoil is from A i Starting from point , move back along the relative velocity direction line S i, locate the appropriate position of the leading edge point. At this point, an aerodynamic pressure difference propeller airfoil plane expansion diagram is completed. Take different r values ​​between the blade root and the blade tip, repeat the above process, and you can get plane expansion diagrams of different radii until the production of one blade is completed. If the propeller needs several blades for the entire circumference, divide them evenly on the same circumference, repeat the above process several times, until the production of several blades is completed.

[0154] The propellers completed above can be arranged into coaxial co-directional twin propellers and coaxial counter-directional twin propellers.

[0155] The coaxial and co-directional double propellers can be formed by repeating the above method to make two single propellers, which are arranged in series.

[0156] The coaxial reverse double propellers are formed by completing the above-mentioned single propeller, dragging the second propeller at a speed in the opposite direction, and then repeating the above method to make another propeller, and arranging the completed two single propellers in series.

Claims

1. An aviation dynamic pressure differential propeller, the cross-sectional development diagram of which includes an upper wing surface and a lower wing surface, characterized in that: The upper wing surface and the lower wing surface section lines are both curved surfaces composed of monotonically descending curves from the leading edge to the trailing edge. At near-sonic and supersonic speeds, the rearward turning angle of the leading edge point of the lower wing surface section line is equal to or greater than the required normal angle of the leading edge point.

2. The aviation dynamic pressure difference propeller according to claim 1, characterized in that: At near-sonic and supersonic speeds, the section line of the lower wing surface is the rearward turning angle from the leading edge to the trailing edge, and the rearward turning angle of the latter point is equal to or greater than the rearward turning angle of the former point.

3. The aviation dynamic pressure difference propeller according to claim 1, characterized in that: At near-sonic and supersonic speeds, the back-turn angle of a spanwise line point is equal to or greater than the required normal angle of the point.

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