A device and method for controlling boundary layer profile and a design method of the device

Abstract

The embodiments of the present application provide a device, method and design method for controlling the boundary layer profile, which relates to the field of fluid mechanics technology, wherein the device comprises: a plurality of channels arranged side by side in the downstream direction of the fluid; each channel comprises an upstream inlet and a downstream outlet, the upstream inlet area of ​​each channel is smaller than the downstream outlet area of ​​each channel, and the downstream outlet area of ​​each channel is the same; the length of each channel decreases successively in the direction away from the wall of the test plate, and the downstream outlet of each channel is on the same straight line; wherein the upstream inlet area, downstream outlet area and length of a single channel satisfy the following conditions: the fluid flowing into the single channel is in a state of conservation of momentum and conservation of flow. The technical solution of the present application can quickly obtain boundary layer flow with a relatively large characteristic scale, that is, obtain boundary layer flow with a relatively high local Reynolds number.

Description

Technical Field

[0001] The present application relates to the technical field of fluid mechanics, and in particular to a device and method for controlling a boundary layer profile, and a design method for the device. Background Art

[0002] The boundary layer is the simplest of all flow phenomena and is the most basic theoretical model in fluid mechanics research. When the boundary layer flow develops downstream, it will experience laminar flow, then the transition stage from laminar flow to turbulent flow, and finally fully develop into turbulent flow. The complex flow phenomena experienced in this process have not yet been fully understood by people.

[0003] In the prior art, in order to make the boundary layer grow rapidly, various flow blocks are used upstream of the boundary layer, which can block the wall flow and reduce the velocity rapidly. (Where, is the mass flow rate of the flow tube, is the fluid density, is the average velocity of the flow, A is the cross-sectional area of ​​the flow tube), the flow area downstream naturally becomes larger, making the boundary layer thicker, but the flow around the flow block is complex and the downstream velocity profile is difficult to control.

[0004] Therefore, in practice, there are usually two major methods to obtain a thicker boundary layer (or a larger characteristic scale): one is to use a very long flow distance to obtain a naturally developed thicker boundary layer, but this requires the test equipment to have a relatively large flow size, which brings greater challenges to the equipment; the other is to set a fixed flow device upstream (such as a triangular flow block), but since the velocity profile obtained by this method does not satisfy the growth law of the boundary layer, it is not suitable for theoretical research. Summary of the invention

[0005] The embodiments of the present application provide a device, method and device design method for controlling the boundary layer profile. The present application is based on the basic boundary layer theory and the flat plate Couette Flow hypothesis, and a thicker boundary layer that meets the specified velocity profile conditions can be obtained through a shorter flow distance.

[0006] Other features and advantages of the present application will become apparent from the following detailed description, or may be learned in part by the practice of the present application.

[0007] According to a first aspect of an embodiment of the present application, there is provided a device for controlling a boundary layer profile, which is disposed on a wall surface of a test plate and comprises: a plurality of channels arranged side by side along a downstream direction of a fluid;

[0008] Each channel comprises an upstream inlet and a downstream outlet, the upstream inlet area of ​​each channel is smaller than the downstream outlet area of ​​each channel, and the downstream outlet area of ​​each channel is the same;

[0009] The length of each channel decreases in the direction away from the wall of the test plate, and the downstream outlet of each channel is on the same straight line;

[0010] The values ​​of the upstream inlet area, the downstream outlet area and the length of a single channel satisfy the following conditions: the fluid flowing into the single channel is in a state of conservation of momentum and conservation of flow.

[0011] In some embodiments of the present application, based on the above solution, the values ​​of the upstream inlet area, downstream outlet area and length of a single channel satisfy the following formula:

[0012] ;

[0013] ;

[0014] ; ;

[0015] in, is the channel inlet flow rate, is the channel outlet flow rate, is the friction correction coefficient of the fluid in a single channel, is the fluid viscosity coefficient, is the volume flow rate of the fluid, is the fluid density, is the downstream outlet area, is the upstream inlet area, is the length, is the average velocity of the fluid in the channel, is the channel outlet flow rate, is the incoming flow velocity.

[0016] In some embodiments of the present application, based on the aforementioned solution, each of the grooves is curved as a whole.

[0017] In some embodiments of the present application, based on the above solution, the average width of each channel increases successively along the direction away from the wall surface of the test plate.

[0018] According to a second aspect of an embodiment of the present application, a method for controlling a boundary layer profile is provided, comprising:

[0019] Calculating the channel parameters of each channel in the device as described in the first aspect according to the control requirements of the boundary layer profile, wherein the channel parameters include: upstream inlet area, downstream outlet area and length;

[0020] Designing the device based on the calculated channel parameters;

[0021] The designed device is arranged at the upstream inlet of the test plate, with the longest channel in the device close to the wall of the test plate.

[0022] According to a third aspect of an embodiment of the present application, a design method of the device according to the first aspect is provided, including:

[0023] Obtain the control requirements of the boundary layer profile and determine the boundary layer profile value;

[0024] Determining channel parameters of a first layer of channels in the device based on the boundary layer profile value, wherein the first layer of channels refers to the longest channel in the device, and the channel parameters include: an upstream inlet area, a downstream outlet area and a length;

[0025] The outlet area of ​​each layer of channels is set to be the same, and the channel parameters of other channels are determined based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value;

[0026] The first layer of grooves is designed according to the groove parameters of the first layer of grooves, and the remaining grooves are designed according to the groove parameters of the remaining grooves;

[0027] The device is obtained by arranging all the channels side by side in descending order of length.

[0028] In some embodiments of the present application, based on the above solution, determining the channel parameters of the first layer of channels in the device based on the boundary layer profile value includes:

[0029] Assume the length of the first layer of channels in the device;

[0030] According to the boundary layer profile value and the length of the first layer of channels, the upstream inlet area and the downstream outlet area of ​​the first layer of channels are determined by the law of conservation of momentum and the law of conservation of flow.

[0031] In some embodiments of the present application, based on the above scheme, the channel parameters of other channels are determined based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value, including:

[0032] Determining downstream outlet areas of other channels based on the downstream outlet areas of the first layer of channels;

[0033] Determining the volume flow of the remaining channels according to the boundary layer profile value and the downstream outlet area of ​​the remaining channels;

[0034] The remaining channels determine their upstream inlet areas and lengths according to their own volume flow rates and downstream outlet areas.

[0035] The technical solution of the present application can quickly obtain a boundary layer flow with a relatively large characteristic scale, that is, obtain a boundary layer flow with a relatively high local Reynolds number.

[0036] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0038] Figure 1 A schematic diagram showing the effect of controlling a boundary layer profile using a device for controlling a boundary layer profile according to an embodiment of the present application is shown;

[0039] Figure 2 A schematic diagram of a flat plate Couette flow according to an embodiment of the present application is shown;

[0040] Figure 3 A schematic diagram of thin channel flow according to an embodiment of the present application is shown. DETAILED DESCRIPTION

[0041] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more comprehensive and complete and fully convey the concept of the example embodiments to those skilled in the art.

[0042] In addition, described feature, structure or characteristic can be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present application. However, those skilled in the art will appreciate that the technical scheme of the present application can be put into practice without one or more of the specific details, or other methods, components, devices, steps, etc. can be adopted. In other cases, known methods, devices, realizations or operations are not shown or described in detail to avoid blurring the various aspects of the application.

[0043] The flowcharts shown in the accompanying drawings are only exemplary and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps can be decomposed, and some operations / steps can be combined or partially combined, so the actual execution order may change according to actual conditions.

[0044] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the objects used in this way can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those shown or described.

[0045] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] Some embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. In the absence of conflict, the following embodiments and features in the embodiments may be combined with each other.

[0047] In view of the technical problems existing in the prior art, an embodiment of the present application provides a device for controlling the boundary layer profile, the device comprising: a plurality of channels arranged side by side along the downstream direction of the fluid;

[0048] Each channel comprises an upstream inlet and a downstream outlet, the upstream inlet area of ​​each channel is smaller than the downstream outlet area of ​​each channel, and the downstream outlet area of ​​each channel is the same;

[0049] The length of each channel decreases in the direction away from the wall of the test plate, and the downstream outlet of each channel is on the same straight line;

[0050] The values ​​of the upstream inlet area, the downstream outlet area and the length of a single channel satisfy the following conditions: the fluid flowing into the single channel is in a state of conservation of momentum and conservation of flow.

[0051] It can be understood that each groove is arranged adjacent to each other, and the thickness of the groove wall between two adjacent grooves is very small, almost approaching zero.

[0052] In some feasible embodiments, based on the above solution, the values ​​of the upstream inlet area, downstream outlet area and length of a single channel satisfy the following formula:

[0053] ; (1)

[0054] ; (2)

[0055] ; (3) ; (4)

[0056] in, is the channel inlet flow rate, is the channel outlet flow rate, is the friction correction coefficient of the fluid in a single channel, is the fluid viscosity coefficient, is the volume flow rate of the fluid, is the fluid density, is the downstream outlet area, is the upstream inlet area, is the length, is the average velocity of the fluid in the channel, is the channel outlet flow rate, is the incoming flow velocity.

[0057] It can be understood that in formulas (1) to (4), , , , are fixed values, so when , and When one of the factors changes, the other two factors will also change. For example, if the downstream outlet area of ​​any channel is known, After that, due to the downstream outlet area of ​​each channel are the same when the length As the size decreases, the upstream inlet area of ​​the channel will increase accordingly, but the upstream inlet area Always smaller than the downstream outlet area , so the upstream inlet area Theoretically, it is infinitely close to the downstream outlet area . Upstream inlet area Infinitely close to the downstream outlet area The corresponding groove is the last groove. As the length of the groove is constantly decreasing, the overall device presents a shape similar to a triangle.

[0058] In some feasible embodiments, based on the above-mentioned solution, each of the grooves is curved as a whole.

[0059] It is understandable that the curve shape of the groove is not fixed, and the curve shape of each groove can be different from each other, but it is necessary to ensure that the grooves are arranged closely and the groove wall thickness between adjacent grooves approaches zero.

[0060] In some feasible embodiments, based on the above solution, the average width of each channel increases in sequence along the direction away from the wall of the test plate.

[0061] Based on the same inventive concept, an embodiment of the present application further provides a method for controlling a boundary layer profile, which is implemented using the device described in the above embodiment. The method includes:

[0062] According to the control requirements of the boundary layer profile, the channel parameters of each channel in the device described in the above embodiment are calculated, and the channel parameters include: upstream inlet area, downstream outlet area and length;

[0063] Designing the device based on the calculated channel parameters;

[0064] The designed device is arranged at the upstream inlet of the test plate, with the longest channel in the device close to the wall of the test plate.

[0065] For example, see Figure 1 , showing a schematic diagram of the effect of controlling the boundary layer profile using a device for controlling the boundary layer profile.

[0066] like Figure 1 As shown, Figure 1 The red part in the figure is a schematic diagram of the structure of a device for controlling the boundary layer profile. The device consists of multiple channels, each of which is arranged along the downstream direction of the fluid. The longest channel is located at the bottom, close to the wall of the test plate, and the remaining channels are arranged in descending order of length, and the downstream outlets of each channel are flush (i.e., on the same straight line). The overall shape of the final device is similar to a triangle.

[0067] like Figure 1 As shown in the figure, the designed device is arranged at the upstream inlet of the test plate. After the flow passes through the test plate and through the device, a thicker boundary layer is obtained at the downstream outlet of the channel in the device, and its velocity profile is Satisfies the given boundary layer velocity profile (such as the Blasius solution of laminar flow, the wall law and loss law of turbulent boundary layer).

[0068] Based on the same inventive concept, an embodiment of the present application also provides a design method for a device for controlling a boundary layer profile. The design method is used to design a device as described in the above embodiment, and the designed device can meet the control requirements of the boundary layer profile.

[0069] Specifically, the method includes:

[0070] Step S100, obtaining the control requirement of the boundary layer profile and determining the boundary layer profile value;

[0071] Step S200, determining channel parameters of a first layer of channels in the device based on the boundary layer profile value, wherein the first layer of channels refers to the longest channel in the device, and the channel parameters include: upstream inlet area, downstream outlet area and length;

[0072] Step S300, setting the outlet area of ​​each layer of channels to be the same, and determining the channel parameters of other channels based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value;

[0073] Step S400, designing the first layer of grooves according to the groove parameters of the first layer of grooves, and designing the remaining grooves according to the groove parameters of the remaining grooves;

[0074] Step S500, all the grooves are arranged side by side in descending order of length to obtain the device.

[0075] In some feasible embodiments, based on the above scheme, determining the channel parameters of the first layer of channels in the device based on the boundary layer profile value includes:

[0076] Assume the length of the first layer of channels in the device;

[0077] According to the boundary layer profile value and the length of the first layer of channels, the upstream inlet area and the downstream outlet area of ​​the first layer of channels are determined by the law of conservation of momentum and the law of conservation of flow.

[0078] In some feasible embodiments, based on the above scheme, the channel parameters of other channels are determined based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value, including:

[0079] Determining downstream outlet areas of other channels based on the downstream outlet areas of the first layer of channels;

[0080] Determining the volume flow of the remaining channels according to the boundary layer profile value and the downstream outlet area of ​​the remaining channels;

[0081] The remaining channels determine their upstream inlet areas and lengths according to their own volume flow rates and downstream outlet areas.

[0082] Below, a specific example of a design approach is provided.

[0083] First, the derivation process of the design principle is as follows:

[0084] Since the channel in this device is relatively thin, the aspect ratio is very large, and the overall curvature is relatively small, the flow therein can be approximated as a flat plate Couette flow in a channel without separation flow. It is believed that a series of normal arranged Coutte flows, after downstream adjustment, eventually form a downstream boundary layer on a macro scale, and the thickness of the boundary layer is related to the normal height of the device.

[0085] For a flat Couette flow, Figure 2 As shown, it flows under the drive of pressure gradient, which is used to overcome the friction stress τ of the wall. w , the basic relationship is:

[0086] ; (5)

[0087] in, h is the half width between the plates, is the coordinate along the height direction, u ( y ) is the velocity profile between the plates, is the average speed, is the volume flow rate, τ w is the friction stress on the wall.

[0088] For the channel flow in this device, Figure 3 A unit thin channel flow is given. Based on the conclusion of flat plate Couette flow, it is assumed that the parameters of each section in the thin channel flow satisfy the above relationship.

[0089] Considering that the cross-sectional area of ​​the channel flow changes along the flow direction, the following relationship is obtained:

[0090] ; (6)

[0091] ; (7)

[0092] Wherein, (6) describes the conservation of mass, is the total flow, is the mass flow rate at the inlet, is the mass flow rate at the outlet. Equation (7) describes the conservation of momentum, is the fluid momentum at the outlet, is the fluid momentum at the outlet, and are the momentum increments generated by the pressure at the inlet and outlet, respectively, is the momentum loss caused by the pressure projection on the surface boundary, is the momentum attenuation caused by wall friction. After sorting, it can be simplified to formula (8):

[0093] ; (8)

[0094] The coefficient 2 before the friction stress on the right side of equation (8) indicates that friction occurs on both the upper and lower sides. Therefore, equations (6) and (8) constitute the governing equations for the flow in a non-separated variable cross-section narrow channel. Referring to the calculation of friction stress in equation (5), it can be assumed that the friction stress can be expressed as:

[0095] ; (9)

[0096] in Cr is the correction factor, indicating the difference between the current friction stress and the Couette flow condition. Cr =1, the same as Couette flow. Cr It should be related to dA. When the area shrinks dA<0, the friction of the flow near the wall increases. Cr >1. The total friction resistance can be obtained by integrating along the channel flow direction. D :

[0097] ; (10)

[0098] Substitute (6) and (9) into (8) and rearrange to get:

[0099] ; (11)

[0100] For equation (11), the flow problem of non-separated variable cross-section channel can be solved, including the following two cases: Case 1: If the flow direction of the thin channel is given and shape A (x), which is directly given by (6) u b ( x ), and the pressure distribution along the path is given by solving (11) p ( x ). Case 2: Given the pressure distribution along the process p ( x ), we can solve equations (6) and (11) and design the pipeline A (x), and calculate u b ( x ).

[0101] For this device, the main requirement is to keep the pressure of the upstream and downstream of the fine groove as close to the incoming flow pressure as possible, which can reduce the impact of the entire device on the flow field outside the boundary layer and reduce the normal velocity of the upstream and downstream of the device. Therefore, each fine groove is designed as a simple expansion flow. Because the expansion of the flow channel reduces the velocity and increases the pressure at the same time, the increased pressure just makes up for the pressure loss caused by the friction of the groove wall. Based on this, it can be considered that the pressure gradient along the flow direction of the fine groove is approximately zero. Substituting it into formula (11), it can be obtained:

[0102] ; (12)

[0103] in, .

[0104] For a single narrow channel, the right side of equation (12) is a constant, and the area of ​​the narrow channel increases linearly along the flow direction, that is:

[0105] ; (13)

[0106] ; (14)

[0107] The total length of the typical jth thin slot is s j , the corresponding volume flow rate is Q j , the upstream inlet velocity is approximately the uniform velocity profile of the free flow, and the average velocity at the downstream outlet is u b,j Satisfying the given boundary layer exit velocity u b ( y ),Right now:

[0108] ; (15)

[0109] in, .

[0110] The upstream inlet area is A in,j , the downstream outlet area is A ex,j , which illustrates the conservation of flow along the narrow channel. As shown in formula (15), it can be further considered that the length of the narrow channel along the flow direction can be calculated by the above formula. s j .

[0111] After knowing the derivation principle, the specific implementation process is as follows:

[0112] (1) Assume that the boundary layer profile to be designed is , which contains the thickness information of the boundary layer:

[0113] The nominal thickness of the boundary layer is δ0; = , is the incoming flow velocity;

[0114] Displacement thickness of the boundary layer ;

[0115] Nominal thickness of the boundary layer ;

[0116] (2) Assume that the length of the thinnest channel in the lowest layer of the device (i.e. the first layer of channels) is s 1;

[0117] (3) The downstream outlet area of ​​the first layer of thin channels is calculated iteratively using equations (13) and (14): A ex,1 and upstream inlet area A in,1 ;

[0118] The outlet center height is y ex,1 = A ex,1 / 2, the corresponding exit velocity is u b ( y ex,1 );

[0119] Volume flow Q 1= u b ( y ex,1 ) A ex,1 = u ∞ A in,1 ;

[0120] Substitute into (14) , the downstream outlet area of ​​the first layer of channels can be solved;

[0121] (4) Assume that the downstream outlet area of ​​each layer of the upper channel is A ex The same as the first layer, and the volume flow rate of each layer of channels is integrated according to formula (15): Q j , the upstream inlet area of ​​the layer is calculated by formula (13) A in,j ;

[0122] (5) Calculate the length of the thin channel of each layer of channel by formula (14): s j .

[0123] (6) After knowing the parameters of all the slots, the device is designed according to the slot parameters.

[0124] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the embodiments disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary techniques in the art that are not disclosed in the present application. It should be understood that the present application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. A device for controlling the boundary layer profile, arranged on the wall of a test plate, characterized in that: include: A plurality of channels arranged side by side along the downstream direction of the fluid; Each channel comprises an upstream inlet and a downstream outlet, the upstream inlet area of ​​each channel is smaller than the downstream outlet area of ​​each channel, and the downstream outlet area of ​​each channel is the same; The length of each channel decreases in the direction away from the wall of the test plate, and the downstream outlet of each channel is on the same straight line; The values ​​of the upstream inlet area, the downstream outlet area and the length of a single channel satisfy the following conditions: the fluid flowing into the single channel is in a state of conservation of momentum and conservation of flow.

2. The device according to claim 1, characterized in that The upstream inlet area, downstream outlet area and length of a single channel satisfy the following formula: ； ； ； ； in, is the channel inlet flow rate, is the channel outlet flow rate, is the friction correction coefficient of the fluid in a single channel, is the fluid viscosity coefficient, is the volume flow rate of the fluid, is the fluid density, is the downstream outlet area, is the upstream inlet area, is the length, is the average velocity of the fluid in the channel, is the channel outlet flow rate, is the incoming flow velocity.

3. The device according to claim 1, characterized in that Each of the grooves is in a curved shape as a whole.

4. The device according to claim 1, characterized in that The average width of each groove increases gradually in the direction away from the wall of the test plate.

5. A method for controlling a boundary layer profile, characterized in that: include: According to the control requirements of the boundary layer profile, calculating the channel parameters of each channel in the device according to any one of claims 1 to 4, the channel parameters including: upstream inlet area, downstream outlet area and length; Designing the device based on the calculated channel parameters; The designed device is arranged at the upstream inlet of the test plate, with the longest channel in the device close to the wall of the test plate.

6. A method for designing a device for controlling a boundary layer profile, characterized in that: include: Obtain the control requirements of the boundary layer profile and determine the boundary layer profile value; Determining channel parameters of a first layer of channels in the device based on the boundary layer profile value, wherein the first layer of channels refers to the longest channel in the device, and the channel parameters include: an upstream inlet area, a downstream outlet area and a length; The outlet area of ​​each layer of channels is set to be the same, and the channel parameters of other channels are determined based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value; The first layer of grooves is designed according to the groove parameters of the first layer of grooves, and the remaining grooves are designed according to the groove parameters of the remaining grooves; The device is obtained by arranging all the channels side by side in descending order of length.

7. The design method according to claim 6, characterized in that: The determining of the channel parameters of the first layer of channels in the device based on the boundary layer profile value comprises: Assume the length of the first layer of channels in the device; According to the boundary layer profile value and the length of the first layer of channels, the upstream inlet area and the downstream outlet area of ​​the first layer of channels are determined by the law of conservation of momentum and the law of conservation of flow.

8. The design method according to claim 7, characterized in that: The determining of the channel parameters of other channels based on the downstream outlet area of ​​the first layer of channels and the boundary layer profile value comprises: Determining downstream outlet areas of other channels based on the downstream outlet areas of the first layer of channels; Determining the volume flow of the remaining channels according to the boundary layer profile value and the downstream outlet area of ​​the remaining channels; The remaining channels determine their upstream inlet areas and lengths according to their own volume flow rates and downstream outlet areas.

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