Bionic airfoil and bionic blade imitating the head profile of an aquatic snake and preparation method thereof

Abstract

The present invention discloses a bionic airfoil, a bionic blade and a preparation method that imitate the profile of an aquatic snake's head, and belongs to the technical field of fluid mechanical equipment. The bionic airfoil of the present invention is obtained by connecting the leading edge of the bionic airfoil and the trailing edge of the basic airfoil. The leading edge of the bionic airfoil is obtained by scaling the contour line of the aquatic snake's head according to the distance H1 between the upper and lower end points of the connection end of the trailing edge of the basic airfoil. The bionic blade of the present invention has an airfoil of the above-mentioned bionic airfoil, and its structure includes a bionic blade front end with a hollow interior, a bionic blade tail, an adjustment mechanism and a flexible connection structure. The connection ends of the bionic blade front end and the bionic blade tail are connected with intervals through the flexible connection structure. The adjustment mechanism is arranged in the cavity of the bionic blade to adjust the motion state of the bionic blade front end. The bionic airfoil of the present invention can prevent rotating impellers and aviation blades from encountering variable working conditions or extreme working conditions during operation, thereby obtaining a blade with better aerodynamic performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of fluid mechanical equipment, and in particular relates to a bionic airfoil and a bionic blade imitating the head profile of an aquatic snake, and a preparation method thereof. Background Art

[0002] In turbomachinery and aviation blades, airfoils serve as the fundamental unit of fluid machinery, and their design determines the performance of the associated equipment. Flow separation is a common phenomenon in airfoil turbulence, affecting the airfoil's fluid dynamics and increasing energy loss. It can also cause dramatic fluctuations in the aerodynamic forces on the airfoil surface, limiting the safe and efficient operation of the associated equipment. Therefore, research on airfoil flow separation control technology is of great significance. To mitigate this phenomenon, bionics, a bridge between nature and science, has made significant progress in improving airfoil aerodynamic performance. By leveraging the inherent structural functions of biological organisms, bionics offers new ideas and methods for the design and manufacture of turbomachinery and aviation blades. Therefore, drawing inspiration from nature to invent various control methods, such as those for energy conservation, drag reduction, noise reduction, and flow separation suppression, will further enhance the design and performance of turbomachinery and aviation blades. Summary of the Invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a bionic airfoil, a bionic blade and a preparation method that imitate the head line of an aquatic snake, so as to avoid rotating impellers and aviation blades encountering variable or extreme working conditions during operation, and obtain blades with better aerodynamic performance.

[0004] To achieve the above-mentioned purpose, the present invention provides the following technical solution: a bionic airfoil that imitates the contour line of an aquatic snake's head, which is obtained by connecting the leading edge of the bionic airfoil and the trailing edge of a basic airfoil. The leading edge of the bionic airfoil is obtained by scaling the contour line of the aquatic snake's head according to the distance H1 between the upper and lower end points of the connection end of the trailing edge of the basic airfoil.

[0005] The present invention also provides a method for preparing a bionic airfoil that imitates the head profile of an aquatic snake, and the specific steps are as follows:

[0006] S1 establishes an xy coordinate system with the most front edge point of the aquatic snake's head as the coordinate origin, obtains the characteristic points of the cross-sectional contour of the aquatic snake's head, and performs nonlinear smooth curve fitting on the characteristic points to obtain the contour line of the aquatic snake's head;

[0007] S2 scales the contour line of the aquatic snake head by a factor of i according to the distance H1 between the upper and lower endpoints of the connection end of the trailing edge of the basic airfoil and the distance H2 between the upper and lower endpoints of the opening end of the contour line of the aquatic snake head to obtain the leading edge of the bionic airfoil;

[0008] S3 connects the connection end of the leading edge of the bionic airfoil and the connection end of the trailing edge of the basic airfoil to obtain a bionic airfoil that imitates the head line of an aquatic snake.

[0009] Furthermore, in S1, the extracted feature points of the aquatic snake head are divided into curve segment A, curve segment B, and curve segment C according to the curvature of the curve, and nonlinear smooth curve fitting is performed on the feature points of the three parts respectively, and fitting curve 1, fitting curve 2, fitting curve 3 and the corresponding control equations y1, y2, and y3 of the fitting curves are obtained, which are as follows:

[0010]

[0011] Among them, k represents the difference between the head features of aquatic snakes of different sizes, y 1k 、y 2k and y 3k Governing equations corresponding to curve fitting for aquatic snake heads of different sizes;

[0012] For the control equation y 1k 、y 2k and y 3k The feature points are discretized and the contour line of the aquatic snake's head is obtained by connecting the obtained feature points in sequence.

[0013] Furthermore, in S2, the fitting curves 1, 2, and 3 are scaled according to the geometric multiple relationship between the distance H1 between the upper and lower endpoints of the connection end of the basic airfoil trailing edge and the distance H2 between the upper and lower endpoints of the opening end of the aquatic snake head contour line, so as to obtain the contour line equations d1, d2, and d3 of the bionic airfoil leading edge applicable to the trailing edge of the basic airfoil:

[0014]

[0015] Where i is the scaling ratio;

[0016] The curves corresponding to the bionic airfoil leading edge contour equations d1, d2, and d3 are sequentially connected to obtain the bionic airfoil leading edge 16.

[0017] Furthermore, the chord length of the trailing edge of the basic airfoil is L2, L2 = (0.6-0.85) × c, where c is the chord length of the basic airfoil.

[0018] The present invention also provides a bionic blade, whose airfoil is the above-mentioned bionic airfoil, and its structure includes a bionic blade front end and a bionic blade tail with a hollow interior, an adjustment mechanism and a flexible connection structure. The connecting ends of the bionic blade front end and the bionic blade tail are connected with intervals through the flexible connection structure, and the adjustment mechanism is arranged in the cavity of the bionic blade to adjust the movement state of the bionic blade front end.

[0019] Furthermore, the flexible connection structure is an elastic flexible skin, and the outer surfaces of the connecting ends of the front end of the bionic blade and the tail end of the bionic blade are connected through the elastic flexible skin.

[0020] Furthermore, the elastic flexible skin is fixed on the outer surface of the connection end between the front end of the bionic blade and the tail end of the bionic blade by fixing screws.

[0021] Furthermore, the adjustment mechanism includes a steering wheel and a servo, the steering wheel is arranged in the front end cavity of the bionic blade through a steering wheel mounting bracket, the servo is fixed in the rear end cavity of the bionic blade through a servo fixing bracket, and the steering wheel is connected to the servo shaft of the servo through a second steering wheel matching hole thereon.

[0022] Furthermore, the front end of the bionic blade has three motion states: downward, intermediate and upward. Specifically:

[0023] The pitch angle in the pitch state is -30°≤θ<0°;

[0024] The angle θ in the intermediate state is 0°;

[0025] The tilt-up angle in the tilt-up state is 0°<θ≤30°.

[0026] Compared with the prior art, the present invention has at least the following beneficial effects:

[0027] The present invention provides a bionic airfoil designed based on the head features of an aquatic snake. As a creature that lives in water, aquatic snakes have developed smooth, fluent, and streamlined head features during their long-term natural evolution. These features give aquatic snakes a unique and efficient drag reduction mechanism and fast, low-noise swimming characteristics. The head of an aquatic snake serves as the frontal surface of the impacting airflow. The incoming flow exerts a large pressure and resistance on the head, but the actual contour of the head of an aquatic snake can effectively alleviate the impact of the incoming flow, effectively divert the flow, and reduce the flow resistance. The leading edge of a conventional airfoil blade, as the frontal surface, will also be subject to a large airflow impact and resistance. Therefore, the bionic airfoil established based on the streamlined characteristic profile of the aquatic snake's head has the advantages of alleviating the impact of the incoming flow, reducing the flow resistance on the airfoil surface, and improving the aerodynamic performance.

[0028] The bionic airfoil obtained above has a higher lift-drag coefficient than conventional airfoils, so the bionic blade fabricated from this airfoil also has better aerodynamic performance. Because aquatic snakes adjust their heads to either an upward or downward pitch to accelerate swimming and reduce flow resistance, the present invention, based on this characteristic, combines the above-mentioned bionic airfoil with an efficient bionic swimming posture to fabricate a bionic blade with an adjustable front end. This bionic blade differs from traditional bionic blades primarily because the front end and the rear end of the bionic blade are not fixedly connected. Instead, a steering wheel and a servo are provided between the front and rear ends of the bionic blade. The steering wheel and the servo cooperate with each other, feeding signals back to the servo according to the blade's operating conditions. The servo responds and drives the steering wheel to rotate. Since the steering wheel and the front end of the bionic blade are fixed together by a steering wheel mounting bracket, a mating hole between the steering wheel and the leading edge of the bionic blade, and a mating hole between the front end bracket and the steering wheel, rotation of the steering wheel also drives rotation of the front end of the bionic blade. Because the front end of the bionic blade needs to complete up-and-down pitching and deflection movements, a certain gap is required between the front and rear ends of the bionic blade. A gap value of 0.04 times L2 ensures that the front end of the bionic blade does not collide with the rear end during pitching and deflecting. However, to further enhance the blade's aerodynamic performance and energy efficiency, the present invention also incorporates an elastic, flexible skin within this gap to reduce drag. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Characteristic diagram of the head of an aquatic snake selected for the present invention;

[0030] Figure 2 This is the feature point extraction diagram of the aquatic snake head of the present invention;

[0031] Figure 3 The figure shows the characteristic points and fitting curve of the head of aquatic snake of the present invention;

[0032] Figure 4 It is the contour line of the leading edge of the bionic airfoil of the present invention;

[0033] Figure 5 This is a diagram showing the process of combining the leading edge of the aquatic snake-like airfoil with the airfoil of the present invention;

[0034] Figure 6 This is a front view of the bionic blade of the present invention;

[0035] Figure 7 This is a top view of the bionic blade of the present invention;

[0036] Figure 8 The side view of the bionic blade of the present invention Figure 1 ;

[0037] Figure 9 The side view of the bionic blade of the present invention Figure 2 ;

[0038] Figure 10 This is a diagram of the leading edge of the bionic blade and related mechanisms of the present invention;

[0039] Figure 11 This is an exploded view of the bionic blade of the present invention;

[0040] Figure 12 This is a diagram of the bionic blade servo of the present invention;

[0041] Figure 13 This is a diagram of the bionic blade rudder of the present invention;

[0042] Figure 14 This is a front end diagram of the bionic blade of the present invention;

[0043] Figure 15 This is a diagram of the tail of the bionic blade of the present invention;

[0044] Figure 16 This is a motion state diagram of the front end of the bionic blade of the present invention;

[0045] Figure 17 This is a flow chart of the movement of the front end of the bionic blade of the present invention;

[0046] In the accompanying drawings: 1-front end of the bionic blade, 2-elastic flexible skin, 3-servo fixing and mounting hole, 4-steering wheel, 5-servo, 6-tail of the bionic blade, 7-elastic flexible skin fixing screw, 8-matching hole between the steering wheel and the leading edge of the bionic blade, 9-servo shaft, 10-servo fixing bracket at the tail of the bionic blade, 11-steering wheel mounting bracket, 12-matching hole between the front end bracket of the bionic blade and the steering wheel, 13-matching hole between the steering wheel and the steering gear shaft, 14-bracket fixing servo hole, 15-basic airfoil trailing edge, 16-bionic airfoil leading edge. DETAILED DESCRIPTION

[0047] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0048] 1. A bionic airfoil imitating the head profile of an aquatic snake is obtained by extracting the head features of an aquatic snake, scaling the head profile proportionally to the dimensions of a basic airfoil to obtain a bionic airfoil leading edge 16, and connecting the scaled bionic airfoil leading edge 16 to the corresponding end points of the connecting ends of the basic airfoil trailing edge 15 to obtain the bionic airfoil imitating the head profile of an aquatic snake. The specific steps are as follows:

[0049] 1) If Figure 1As shown in the figure, in order to extract the head features of aquatic snakes, CT scans were performed on actual aquatic snake samples to obtain the three-dimensional structural features of the head of the actual aquatic snake samples. The length of the aquatic snake head was selected as L1. The inverse reconstruction method was used to establish an xy coordinate system with the most front edge point of the aquatic snake head as the coordinate origin, and the characteristic points of the cross-sectional contour of the aquatic snake head were extracted (x, y). The extraction results are shown in the figure. Figure 2 shown.

[0050] 2) In order to express the extracted feature points with parameters, the extracted feature points of the aquatic snake head are divided into three parts: curve segment A, curve segment B and curve segment C according to the curve curvature characteristics. Nonlinear smooth curve fitting is performed on the feature points of the three parts respectively, and fitting curve 1, fitting curve 2, fitting curve 3 and the corresponding control equations y1, y2 and y3 of the fitting curves are obtained, as shown in the following figure: Figure 3 As shown;

[0051] The fitting curve equations corresponding to fitting curve 1, fitting curve 2, and fitting curve 3 are as follows:

[0052]

[0053] The above y 1k 、y 2k and y 3k These are the equations corresponding to fitting curve 1, fitting curve 2, and fitting curve 3, respectively. Fitting curve 1 corresponds to curve segment A, fitting curve 2 corresponds to curve segment B, and fitting curve 3 corresponds to curve segment C. The above equations are applicable to the head contour equations of aquatic snakes of different sizes, where k represents the degree of difference between the head features of aquatic snakes of different sizes, and k = 0.3 to 2.

[0054] 3) If Figure 4 As shown, the control equations y1, y2 and y3 are discretized, and the 16 characteristic points of the leading edge of the bionic airfoil are connected in sequence to obtain the contour line of the aquatic snake head;

[0055] 4) The contour line of the aquatic snake head is scaled by a factor of i based on the distance H1 between the upper and lower endpoints of the connection end of the basic airfoil trailing edge 15 and the distance H2 between the upper and lower endpoints of the opening end of the contour line of the aquatic snake head. This yields a bionic airfoil leading edge 16 that can be applied to existing airfoils. Specifically:

[0056] By scaling the equations of fitting curve 1, fitting curve 2, and fitting curve 3 by a factor of i according to the geometric multiple relationship between H1 and H2, the equations of the bionic airfoil leading edge contour line d1, d2, and d3 applicable to the basic airfoil of a specific size can be obtained:

[0057]

[0058] Where i is the scaling factor.

[0059] 5. Such as Figure 5 As shown, the basic airfoil is divided into a basic airfoil leading edge and a basic airfoil trailing edge 15. The basic airfoil leading edge is replaced by a bionic airfoil leading edge 16 to obtain a bionic airfoil. According to the proportion of the chord length occupied by the simulated snake head profile at the airfoil leading edge, the chord length of the basic airfoil trailing edge 15 is estimated to be L2, L2 = (0.6-0.85) × c, where c is the chord length of the basic airfoil.

[0060] 2. Based on the above-mentioned bionic airfoil, the present invention also prepares a bionic blade with a dynamically adjustable leading edge. The surface of the bionic blade adopts an elastic and flexible skin to achieve a smooth transition. Under different working conditions, by controlling the front end of the bionic blade to perform pitching motion at different angles, the blade can have higher aerodynamic performance and improve energy utilization. Specifically:

[0061] 1) The above-mentioned bionic blade is a bionic blade with dynamically adjustable leading edge. Because aquatic snakes are one of the aquatic animals that can swim fast, with low swimming resistance and low swimming noise, their head contour structure is special and they move fast. When encountering prey, their heads will adjust to an upward or downward posture to accelerate swimming (such as Figure 1 (as shown in the left image) to further reduce the resistance of the surrounding fluid on its head, suppress swimming noise, and improve swimming efficiency, thereby providing it with a good hydrodynamic advantage during predation attacks and increasing its success rate. Therefore, the present invention has designed a bionic blade with a dynamically adjustable leading edge to further improve its aerodynamic performance. This blade is designed and manufactured based on a predetermined bionic airfoil profile by axially stretching the skin, and the blade has a hollow structure in the middle.

[0062] 2) If Figures 6-9 As shown, the bionic blade of the present invention is obtained by connecting the internal hollow bionic blade front end 1 and the bionic blade tail 6 with intervals through a flexible connection structure. The cross-sectional linear contour of the bionic blade front end 1 is a bionic airfoil leading edge 16. An adjustment mechanism is also provided in the inner cavity of the above-mentioned bionic blade. In order to smoothly connect the surface of the bionic blade front end 1 and the bionic blade tail 6 and reduce resistance, a certain gap needs to be left between the bionic blade front end 1 and the bionic blade tail 6. The gap value is 0.04 times L2, which can ensure that when the bionic blade front end is raised or lowered, there is no collision between the bionic blade tail and the bionic blade front end.

[0063] The present invention connects the bionic blade front end 1 and the bionic blade tail 6 through an elastic flexible skin 2. The elastic flexible skin structure 2 can expand and contract to varying degrees according to the rotation of the bionic leading edge, thereby reducing flow resistance and surface non-smoothness.

[0064] like Figures 10-15As shown, the adjustment mechanism includes a steering wheel 4, a steering gear 5, a first steering wheel matching hole 8, a steering gear shaft 9, a steering gear fixing bracket 10, a steering wheel mounting bracket 11, a bracket matching hole 12, and a second steering wheel matching hole 13;

[0065] A steering wheel mounting bracket 11 is fixed in the inner cavity of the front end 1 of the bionic blade, and a first steering wheel matching hole 8 is provided at one end of the steering wheel 4. The steering wheel 4 and the steering wheel mounting bracket 11 are fixedly connected through the first steering wheel matching hole 8 and the bracket matching hole 12 on the steering wheel mounting bracket 11; a second steering wheel matching hole 13 is provided at the other end of the steering wheel 4, and the second steering wheel matching hole 13 is used to connect with the steering gear shaft 9 to realize the connection between the steering wheel 4 and the steering gear 5.

[0066] The servo 5 is provided with a servo fixing installation hole 3, and the servo fixing bracket 10 is provided with a bracket fixing servo hole 14. The servo 5 is fixed in the inner cavity of the bionic blade tail 6 through the fixed installation hole 3 on the servo 5 and the bracket fixing servo hole 14 on the servo fixing bracket 10.

[0067] The cooperation between the steering wheel 4 and the steering gear 5 of the present invention enables the leading edge of the bionic blade to perform pitch and deflection motions according to different working conditions, thereby improving the aerodynamic performance of the blade.

[0068] Preferably, the elastic flexible skin 2 is fixed to the outer surface of the connection end between the front end 1 of the bionic blade and the tail end 6 of the bionic blade by fixing screws 7 .

[0069] When aquatic snakes are hunting or escaping from enemies, their heads will be adjusted to an upward or downward pitch to accelerate swimming, thereby further reducing the head's head flow resistance, suppressing the generation of swimming noise, and improving swimming efficiency. Based on this bionic pitch state, the front end of the bionic blade of the present invention can have three motion states, namely downward pitch, intermediate state, and upward pitch. The motion adjustment process of the front end of the bionic blade is as follows: Figure 17 .

[0070] The front end of the bionic blade pitches down: Based on the feedback and evaluation of the operating conditions by the aerodynamic performance detection mechanism, the front end of the bionic blade is adjusted to pitch down to improve the aerodynamic performance of the blade and increase energy utilization. The signal is fed back to the steering gear 5, which responds by driving the steering wheel 4 to rotate and complete the pitching movement together with the bionic leading edge blade 1 and the steering wheel mounting bracket 11, while the tail of the bionic blade 6 remains in its original state. Figure 16 As shown, the downward angle of the front end of the bionic blade in the downward-dipping state in the present invention is -30°≤θ<0°.

[0071] The bionic blade front end intermediate state: Based on the operating conditions, the bionic blade front end does not need to pitch to improve the blade's aerodynamic performance and energy utilization. This signal is fed back to the servo 5, but the servo 5 does not respond, the steering wheel 4 does not rotate, the bionic leading edge blade 1 and the steering wheel mounting bracket 11 remain in their original state, and the bionic blade tail 6 also remains in its original state. In the present invention, the angle θ of the bionic blade front end intermediate state is 0°.

[0072] Bionic blade front end tilted up state: According to the operating conditions, the front end of the bionic blade needs to tilt up to improve the aerodynamic performance of the blade and improve energy utilization. The signal is fed back to the steering gear 5, which responds and drives the steering wheel 4 to rotate together with the bionic leading edge blade 1 and the bionic blade front end steering wheel mounting bracket 11 to complete the tilting movement, while the bionic blade tail 6 remains in its original state. The tilting angle of the bionic blade front end in the present invention is 0°

Claims

1. A bionic airfoil imitating the head profile of an aquatic snake, characterized in that: The bionic airfoil leading edge (16) is connected to the basic airfoil trailing edge (15), wherein the bionic airfoil leading edge (16) is connected to the basic airfoil trailing edge (15) at a distance between the upper and lower end points of the connection end. H 1. Obtained by scaling the outline of the aquatic snake's head; The specific steps for preparing the bionic airfoil imitating the head profile of an aquatic snake are as follows: S1 establishes an xy coordinate system with the most front edge point of the aquatic snake's head as the coordinate origin, obtains the characteristic points of the cross-sectional contour of the aquatic snake's head, and performs nonlinear smooth curve fitting on the characteristic points to obtain the contour line of the aquatic snake's head; S2 is the distance between the upper and lower ends of the connection end of the trailing edge (15) of the basic airfoil. H 1 is the distance between the upper and lower ends of the opening end of the aquatic snake's head outline H 2. Make the outline of the aquatic snake's head i times the scale to obtain the bionic airfoil leading edge (16); S3 connects the connection end of the bionic airfoil leading edge (16) and the connection end of the basic airfoil trailing edge (15) to obtain a bionic airfoil that imitates the head line of an aquatic snake; In S1, the extracted feature points of the aquatic snake head are divided into curve segment A, curve segment B, and curve segment C according to the curve curvature characteristics. Nonlinear smooth curve fitting is performed on the feature points of the three parts, and fitting curve 1, fitting curve 2, fitting curve 3 and the corresponding control equations y1, y2, and y3 of the fitting curves are obtained as follows: in, k Indicates the difference between the head features of aquatic snakes of different sizes, y 1k 、 y 2k and y 3k Governing equations corresponding to curve fitting for aquatic snake heads of different sizes; For the control equation y 1k 、 y 2k and y 3k The characteristic points are discretized and the contour line of the aquatic snake's head is obtained by connecting the obtained characteristic points in sequence; In S2, the distance between the upper and lower end points of the connection end of the basic airfoil trailing edge (15) is H 1 is the distance between the upper and lower ends of the opening end of the aquatic snake's head outline H 2, the geometric multiple relationship between fitting curves 1, 2, and 3 is scaled to obtain the contour line equation of the bionic airfoil leading edge applicable to the basic airfoil trailing edge (15). d 1. d 2. d 3: in, i is the scaling ratio; The bionic airfoil leading edge contour equation d 1. d 2. d 3 corresponding curves are sequentially connected to obtain the bionic airfoil leading edge 16; The chord length of the basic airfoil trailing edge (15) is L 2, ,in, c is the chord length of the basic airfoil.

2. A bionic blade, characterized in that: Its airfoil is the bionic airfoil as claimed in claim 1, and its structure includes a bionic blade front end (1) and a bionic blade tail (6) with a hollow interior, an adjustment mechanism and a flexible connection structure. The connection ends of the bionic blade front end (1) and the bionic blade tail (6) are connected with intervals through the flexible connection structure, and the adjustment mechanism is arranged in the cavity of the bionic blade to adjust the motion state of the bionic blade front end (1).

3. The bionic blade according to claim 2, characterized in that: The flexible connection structure is an elastic flexible skin (2), and the outer surfaces of the connection ends of the bionic blade front end (1) and the bionic blade tail end (6) are connected via the elastic flexible skin (2).

4. The bionic blade according to claim 3, characterized in that: The elastic flexible skin (2) is fixed to the outer surface of the connection end between the front end (1) of the bionic blade and the tail end (6) of the bionic blade by means of fixing screws (7).

5. The bionic blade according to claim 2, characterized in that: The regulating mechanism comprises a steering wheel (4) and a steering gear (5); the steering wheel (4) is arranged in the inner cavity of the front end (1) of the bionic blade via a steering wheel mounting bracket (11); the steering gear (5) is fixed in the inner cavity of the rear end (6) of the bionic blade via a steering gear fixing bracket (10); and the steering wheel (4) is connected to the steering gear shaft (9) of the steering gear (5) via a second steering wheel matching hole (13) thereon.

6. The bionic blade according to claim 2, characterized in that: The front end of the bionic blade (1) has three motion states, namely, downward pitch, intermediate state and upward pitch. Specifically: Pitch-down angle ; The angle of the intermediate state ; Tilt-up angle in tilt-up state .

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