A Design Method for Microstructures in a Gas Wave Channel with Pressure Boosting and Vortex Suppression

Abstract

The design method of the micro-structure in the gas wave channel for pressurization and vortex elimination of the present invention belongs to the technical field of pressurization of a rotating hub type shock wave refrigerator, and relates to a design method of the micro-structure in the gas wave channel for pressurization and vortex elimination. This method first constructs a numerical simulation model of the gas wave tube to analyze the gas flow state during the refrigeration cycle of the channel and analyze the cause of the turbulent vortex at the leading edge of the channel during the high-pressure intake stage. Secondly, based on the passive control theory of wall turbulence, the thickness of the viscous sublayer at large Reynolds numbers and the actual channel interval thickness, the feasible processing size range of the tube wall micro-structure is determined, and orthogonal simulation comparison is carried out to analyze the specific influence of the micro-structure morphology under different depth-width ratios on the turbulent vortex. Finally, the optimal micro-structure size parameters for pressurization and vortex elimination are obtained. This method has the characteristics of strong versatility, simple calculation process, high processing feasibility, etc. Without changing the macroscopic flow characteristics of the existing channel, this method has important practical application value for improving the refrigeration efficiency of the gas wave refrigerator.

Description

Technical Field

[0001] The present invention belongs to the technical field of supercharging of a rotary shock refrigerating machine, and relates to a design method for a microstructure in a gas wave flow passage for supercharging and vortex elimination. Background Art

[0002] A gas wave refrigerating machine is a new type of refrigerating equipment that uses the expansion of the pressure energy of a gas itself for refrigeration. It has the advantages of high expansion efficiency, low maintenance cost, and the ability to operate with liquid carried, etc. Therefore, it has a broader development prospect compared with a turbine refrigerating machine with high cost and complex maintenance. The overall structure of a rotary gas wave refrigerating machine is relatively simple, mainly composed of a high-speed gas wave rotor and an external circulation structure, and it has wide applications in many fields such as natural gas dehydration and purification, liquid hydrocarbon recovery, and chemical tail gas recovery. However, in the refrigeration process, the internal flow characteristics, thermodynamic effects, and their interaction of the basic unit in the gas wave machine rotor - the gas wave tube are very complex. The shape factors of the gas wave tube have a great influence on the flow characteristics of the gas in the flow passage, thereby changing the isentropic expansion ratio of the gas wave machine. Accordingly, various modifications of the gas wave tube to improve the refrigeration efficiency of the gas wave refrigerating machine are the key research directions at home and abroad for a long time.

[0003] At present, the structural modification of the gas wave tube mostly focuses on the macroscopic scale, so the optimization design of the cross-sectional shape of the tube flow is mostly studied. In the prior art document 1, the patent of Liu Peiqi et al. with the publication number CN206803547U, "A double-opening variable cross-section gas wave refrigerating machine", uses the variable cross-section structure in the gas wave tube to make the reflected expansion wave occur without being interfered by the reflected shock wave or the reverse compression wave, enhancing the intensity of the reflected expansion wave. However, at the same time, it suppresses the transmission intensity of the forward shock wave, reduces the expansion depth of the gas after the wave, and weakens the temperature drop value of the pre-cooled gas; in the prior art document 2, the patent of Zou Jiupeng et al. with the publication number CN205448390U, "A middle wave blocking cavity isolated gas wave tube", sets a wave blocking cavity with a limited volume in the middle section of each gas wave tube. Its two ends are respectively connected and communicated with the front section and the rear section of the gas wave tube, and a flow passage that first expands and then contracts is formed inside, making the internal through-flow cross-sectional area of the front section of the gas wave tube smaller than that of the rear section of the tube. The reflected shock wave in the tube is buffered and the energy is dissipated in the wave blocking cavity, reducing the direct heating of the already refrigerated gas. However, the wave blocking cavity will dissipate the pressure energy of the high-pressure inlet gas. Summary of the Invention

[0004] Aiming at the defect that it is difficult to suppress the mixing loss of high and low pressure gases in the flow channel during the modification of the gas wave tube at the macroscopic scale, the present invention aims to add microstructures to the inner wall surface of the gas wave tube without changing the macroscopic morphology of the gas wave tube, so as to overcome the pressure energy consumption and gas mixing caused by the turbulent vortices during the high-pressure intake stage of the gas wave tube. Starting from the establishment of a single-channel calculation model of the gas wave tube and the numerical simulation of the flow state during a single refrigeration cycle of the flow channel, the research on the origin and influence of turbulent vortices during the continuous high-pressure intake stage of the flow channel is carried out, and a design method for the microstructures in the gas wave flow channel with pressure boosting and vortex reduction is invented. This method is improved on the basis of the basic morphology of a conventional-sized gas wave machine. Taking the frictional resistance of the gas wave tube flow and the thickness of the turbulent viscous sublayer in the tube as the constraint conditions, the interval of the microstructure size parameters is obtained. Multiple groups of orthogonal comparison simulation schemes with the depth / width factor as the variable are designed, an evaluation method for the pressure boosting and vortex reduction effect is established, and the microgroove depth-width matching size parameters with the best pressure boosting and vortex reduction effect are obtained by comparing the simulation results. The pressure-boosting microstructures designed on the inner wall surface of the gas wave tube by this method induce momentum exchange in the near-wall vortex system, effectively reducing the intensity of the largest turbulent vortices in the mainstream, reducing the loss of pressure energy converted into vortex kinetic energy, and having practical application value for improving the isentropic refrigeration efficiency of the rotary gas wave refrigerator.

[0005] The technical solution adopted by the present invention is a design method for the microstructures in the gas wave flow channel with pressure boosting and vortex reduction. The method is characterized in that, firstly, a calculation model of the gas wave tube is constructed to calculate the jet loss during the high-pressure jet stage of the flow channel, analyze the origin of the turbulent vortices at the leading edge of the flow channel during the intake process, and characterize the average friction coefficient of the inner wall of the gas wave tube; secondly, based on the passive control theory of wall turbulence, considering the thickness of the viscous sublayer of the flow channel and the actual cross-sectional area of the flow channel, the optimization interval of the microstructure size of the pipe wall is determined; then, orthogonal simulation comparison is carried out to analyze the specific influence of the microstructure morphology under different depth-width ratios on the turbulent vortices; finally, an evaluation standard for the pressure boosting and vortex reduction effect is established, and the optimal microstructure size parameters for pressure boosting and vortex reduction are obtained according to the standard. The specific steps of the method are as follows:

[0006] Step 1: Construct a calculation model for the flow characteristics of the gas wave tube

[0007] a) Calculate the equivalent diameter d of the gas wave tube t

[0008] Based on the analysis of the fluid flow state in the gas wave tube, first simplify the gas wave tube 2 in the runner 1 into a one-dimensional gas wave tube. Let the width of the flow channel in the gas wave tube be W t , the chord length of the bottom arc surface be L t , and the angle occupied by the axial arrangement be α t . Therefore, the cross-sectional area A of the gas wave tube t is:

[0009]

[0010] The wetted perimeter χ t is:

[0011]

[0012] Using the cross-sectional area of water flow in the pipe, which is four times A t and the wetted perimeter χ of the pipe cross-section t the ratio is used as the equivalent diameter d of the simplified gas wave tube t :

[0013]

[0014] b) Mathematically describe the intake nozzle of the gas wave tube, and calculate the turbulent kinetic energy generated due to jet loss and the jet loss during the gradually opening and closing stage

[0015] The high-pressure outlet nozzle 4 is a constant-pressure outlet end. Simplify the velocity distribution of the high-pressure intake nozzle 3, ignoring the body force of the gas in the flow channel. The velocity distribution at the nozzle is a one-dimensional Poiseuille type:

[0016]

[0017] where v1 is the velocity of the intake nozzle, μ is the air dynamic viscosity coefficient in this state, k1 is the proportional correction coefficient of the nozzle velocity, which needs to be corrected according to the actual measurement experiment results, D is the nozzle diameter, and y is the vertical distance from a point inside the nozzle to the lower wall of the pipe

[0018] Let h j be the turbulent kinetic energy of the gas wave tube. The kinetic energy equation is obtained from the velocity difference between the high-pressure intake nozzle 3 and the high-pressure outlet nozzle 4:

[0019]

[0020] where k2 is the proportional correction coefficient of the turbulent kinetic energy loss, g is the local acceleration of gravity, v2 is the velocity of the outlet nozzle, A1 is the relative cross-sectional area when the nozzle and the flow channel gradually open, and A2 is the cross-sectional area of water flow in the pipe, that is, A t . Using formula (5) to calculate the turbulent kinetic energy generated due to jet loss to describe the magnitude of the jet loss during the gradually opening and closing stage. This part of the loss is manifested in the form of turbulent vortices. If the turbulent kinetic energy loss is greater, the size and vortex kinetic energy of the turbulent vortices are greater

[0021] Step 2. Characterize the average friction coefficient of the inner wall of the gas wave tube

[0022] Analyze the control volume 7 with a length of dx in the leading edge of the gas wave tube with an axial length of L in the one-dimensional gas wave tube. Let the tangential stress of the wall on the gas be τ w , the critical sound speed be c cr , and γ be the adiabatic coefficient of air in this state; let the cross-sectional velocity coefficient in the control volume 7 be M * = v / c cr, Ma is the fluid Mach number at the cross-section in the control volume 7, v is the fluid flow velocity at the cross-section of the control volume 7, and:

[0023]

[0024] Define the friction resistance coefficient of the pipe inner wall as C f , τ w is the tangential stress of the wall on the gas, ρ is the density of air in this state, υ is the specific volume of air, then the friction resistance coefficient of the pipe inner wall is:

[0025]

[0026] List the momentum equation for the control volume 7 and integrate to obtain:

[0027]

[0028] Among them, M *1 is the cross-section velocity coefficient at the intake end face 5, M *2 is the cross-section velocity coefficient at the intake end face 6, so:

[0029]

[0030] Use formula (6) to substitute Ma 2 for M * 2 , assume the gas Mach number Ma1 at the intake end face 5 of the control volume and the gas Mach number Ma2 at the outlet end face 6 of the control volume, and the average friction resistance coefficient The calculation formula is:

[0031]

[0032] Finally, the average friction coefficient is characterized by the Mach numbers at the intake end face 5 and the outlet end face 6

[0033] Step 3. Design of the size parameters of the rectangular cross-section microstructure in the flow direction

[0034] Utilize the vortex-shedding characteristics of the microstructure in the flow direction to design a rectangular cross-section microstructure 2b on the inner wall surface 2a of the gas wave tube. The constraint conditions for the microstructure size are:

[0035] 1) The designed depth D m needs to be greater than the thickness δ of the viscous sublayer. Calculate the thickness δ of the viscous sublayer of the gas wave tube:

[0036]

[0037] 2) If the rectangular cross-section microstructure 2b in the flow direction needs to effectively interfere with the vortex system coherent structure generated by the incident loss, then the microstructure spacing S mIt is required to be less than 20δ, and the width W of the microstructure m should be greater than 5δ. At the same time, the inner wall perimeter of the gas wave tube 2 is χ t , and the number of microstructures is jointly determined according to the above conditions and actual situations.

[0038] 3) Considering that the high-pressure incident air flow generated at the high-pressure intake nozzle 3 is in a one-dimensional Poiseuille type distribution, in order to expand the vortex-shedding reduction characteristics of the rectangular cross-section microstructure 2b in the downstream direction, it is necessary to arrange the rectangular cross-section microstructure 2b in the flow channel at a certain offset angle α. The calculation method of the offset angle α is as follows:

[0039]

[0040] where Re is the Reynolds number of the gas in the flow channel, and A fa is the actual free flow area in the gas wave tube 2, that is, A t , and A fn is the nominal flow area based on the inner diameter of the tube after adding the microstructure, which is the free flow area plus the increased area after adding the microstructure.

[0041] Combining the above conditions and formulas, the specific design parameter ranges of the depth, spacing, width, offset angle, and number of microstructures are obtained.

[0042] Step Four: Select the microstructure size parameters with different depth-width combinations and conduct orthogonal comparison experiments;

[0043] Select M groups of size parameters with different depth-width combinations from the above-calculated microstructure size ranges for orthogonal simulation comparison experiments; use 3D modeling software to establish the overall model of the rotating hub and import it into Fluent, extract the single-channel flow channel fluid domain, and divide structured grids. According to the actual operating conditions, that is, design boundary conditions such as pressure inlet - pressure outlet, select the large eddy simulation (LES) model for dynamic simulation.

[0044] Step Five: Establish an evaluation criterion for the supercharging and vortex-shedding reduction effect to obtain the optimal microstructure parameter combination conditions;

[0045] Use the Q criterion to calibrate the maximum eddy kinetic energy intensity and give the influence of the microstructure gas wave tube flow channel with different depth-width combination size parameters on the eddy kinetic energy; use the ratio of the maximum eddy viscosity intensity Ω Max to the maximum eddy viscosity intensity Ω Max' of the microstructure flow channel as the evaluation criterion to establish an evaluation method for the supercharging and vortex-shedding reduction effect, that is:

[0046]

[0047] Finally, according to the results of the orthogonal simulation experiment comparison, the size parameters of the microgroove depth-width combination with the best supercharging and vortex-shedding reduction effect are obtained.

[0048] The remarkable effects and benefits of the present invention are aimed at the practical problems such as insufficient expansion depth of the rotary drum type gas wave refrigerator and the change of flow characteristics after macroscopic modification. Starting from the numerical calculation model, a design method for the microstructural parameters of the inner wall surface pressurization and vortex reduction of the gas wave tube based on the theory of passive control of wall turbulence is invented. It is improved on the basis of the basic shape of the gas wave machine with conventional dimensions. Taking the friction resistance of the tube flow in the gas wave tube and the thickness of the turbulent viscous sublayer in the tube as the constraint conditions, the microstructural size range is obtained. Multiple sets of orthogonal comparison simulation schemes with the depth / width factor as the variable are designed, and an evaluation method for the effect of pressurization and vortex reduction is established. By comparing the simulation results, the microgroove depth-width matching size parameters with the best pressurization and vortex reduction effect are obtained. Without changing the macroscopic flow characteristics of the existing flow channel, the turbulent vortex intensity of the mainstream is passively controlled. This method has the characteristics of strong versatility, simple calculation process, high processing feasibility, etc. Without changing the macroscopic flow characteristics of the existing flow channel, the pressurization microstructure on the inner wall surface of the gas wave tube induces momentum exchange in the near-wall vortex system, effectively reducing the intensity of the largest turbulent vortex in the mainstream, reducing the loss of pressure energy converted into vortex kinetic energy, and has practical application value for improving the isentropic refrigeration efficiency of the rotary drum type gas wave refrigerator. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flowchart of a design method for the microstructure of a gas wave flow channel with pressurization and vortex reduction.

[0050] Figure 2 It is the front view of the rotary drum structure, Figure 3 It is the three-dimensional partial cross-sectional view of the rotary drum structure. Among them, 1 - rotary drum, 1a - air passage, 2 - gas wave tube, 2a - inner wall surface of the gas wave tube, 2b - rectangular cross-sectional microstructure along the flow direction, 3 - high-pressure intake nozzle, 4 - high-pressure outlet nozzle. α t - Axial arrangement angle of the existing gas wave tube.

[0051] Figure 4 It is a diagram of the one-dimensional gas wave tube flow analysis model, where 2 - gas wave tube, 5 - intake end face, 6 - outlet end face, 7 - control volume, L - axial length of the gas wave tube (mm), dx - length of the control volume 7 (mm), x - distance from the control volume 7 to the inlet end (mm).

[0052] Figure 5 It is a microstructural diagram of the gas wave tube, Figure 6 It is a schematic cross-sectional view of the microstructure. Among them, 2a - inner wall surface of the gas wave tube, 2b - rectangular cross-sectional microstructure along the flow direction, D m - Design depth of the gas wave tube microstructure, S m - Microstructure spacing, W m - Microstructure width, α - offset angle of the gas wave tube microstructure.

[0053] Figure 7It is a diagram showing the influence of the micro-structure size on the maximum vorticity kinetic energy in the flow channel. Among them, Curve 1 shows the variation of the maximum vorticity kinetic energy with the micro-structure width w when the micro-structure depth d = 0.1 mm; Curve 2 shows the variation of the maximum vorticity kinetic energy with the micro-structure width w when the micro-structure depth d = 0.2 mm; Curve 3 shows the variation of the maximum vorticity kinetic energy with the micro-structure width w when the micro-structure depth d = 0.3 mm; Curve 4 shows the variation of the maximum vorticity kinetic energy with the micro-structure width w when the micro-structure depth d = 0.4 mm; Curve 5 shows the variation of the maximum vorticity kinetic energy with the micro-structure width w when the micro-structure depth d = 0.5 mm. Detailed implementation manners

[0054] The following describes in detail the specific implementation manners of the present invention in combination with the technical solutions and the drawings.

[0055] Appendix Figure 1 It is a flowchart of the design method for the micro-structure of the pressure-boosting and vortex-suppressing gas wave flow channel of the present invention. Aiming at the disadvantages such as insufficient expansion efficiency of the gas wave refrigerator resulting in reduced refrigeration efficiency, the numerical simulation is combined with the theoretical calculation to clarify the influence of the gas flow state in the gas wave tube on the refrigeration efficiency, and the gas wave tube pressure-boosting and vortex-suppressing method for passively controlling the turbulent vortex intensity on the inner wall surface of the gas wave tube is realized. This method first constructs a calculation model of the gas wave tube, analyzes the gas flow state during the refrigeration cycle of the flow channel, and analyzes the cause of the turbulent vortex at the leading edge of the flow channel during the high-pressure intake stage; secondly, considering factors such as the passive control theory of wall turbulence and the thickness of the viscous sublayer, the specific design parameter range of the micro-structure is obtained; the orthogonal simulation comparison is carried out to compare the specific influence of the micro-structure morphology under different depth-to-width ratios on the turbulent vortex; a standard for evaluating the pressure-boosting and vortex-suppressing effect is established, and finally the optimal micro-structure size parameters for pressure-boosting and vortex-suppressing are obtained. The specific steps of the design method flow are as follows:

[0056] Step 1: Construct a calculation model for the flow characteristics of the gas wave tube

[0057] Select the existing hub structure of the core component of the rotary gas wave refrigerator as shown in Appendix Figure 2 , Figure 3 . In the existing hub 1, the width W of the air passage 1a in the gas wave tube 2 is t = 10 mm, the chord length L of the bottom arc surface is t = 9.96 mm, the axial arrangement angle α of the gas wave tubes is t = 7°. Use formulas (1) and (2) to calculate the cross-sectional area A t and the wetted perimeter χ t of the gas wave tube, and obtain the cross-sectional area A t of the gas wave tube as 188.15 mm 2 and the wetted perimeter χ t as 54.88 mm. Use formula (3) to calculate the equivalent diameter d t of the gas wave tube = 12.3 mm.

[0058] When the hub operates at a rotational speed of 2900 rpm, the intake pressure at the high-pressure intake nozzle 3 is 0.26 MPa, and the intake temperature is 275 K. According to the intake temperature of 275 K and the intake pressure of 0.26 MPa of the ideal gas, the dynamic viscosity μ of the high-pressure intake can be obtained, and it is approximately taken as 2×10 -5 Pa·s.

[0059] The proportional correction coefficient k1 of the nozzle velocity is taken as 26 according to the actual situation, and the inner diameter D of the nozzle pipe is 0.04 m. Substituting the above data into formula (4), the mathematical simplified model of the high-pressure intake nozzle 3 can be obtained. The kinetic energy equation is listed with the velocity difference between the inlet end and the outlet end to solve the turbulent kinetic energy h j of the gas wave tube. Substituting the simplified nozzle velocity distribution v1 into formula (5), combined with the proportional correction coefficient k2 of the turbulent kinetic energy loss = 9.7×10 -5 The maximum turbulent kinetic energy of the jet loss in the gradually opening and closing stage is calculated to be 0.079 J, which is used to compare the vortex elimination effect of the subsequent microstructures.

[0060] Step 2: Characterize the average friction coefficient of the inner wall of the gas wave tube

[0061] The simplified one-dimensional gas wave tube flow analysis model of the gas wave tube 2 in the rotating hub 1 is as Figure 4 shown. Take a length of dx = 3 mm in the leading edge of the one-dimensional gas wave tube with an axial length L = 40 mm for analysis based on the control volume 7 at the inlet end x = 10 mm. According to the intake temperature of 275 K and the intake pressure of 0.26 MPa of the ideal gas, the critical sound speed can be obtained as 439.6626 m / s, and the Reynolds number Re is 244542. The adiabatic coefficient γ of air in this state is 1.3197. Let the cross-sectional velocity coefficient in the control volume be M * = v / c cr , and it is calculated using formula (6).

[0062] Let the density ρ of air be 2.7092 kg / m 3 , and the friction resistance of the tube inner wall is calculated as C f using formula (7). The momentum equation of the control volume 7 is listed and integrated using formulas (8) and (9), and formula (6) is applied to substitute M a 2 for M * 2 . Let the gas Mach number Ma1 at the intake end face 5 of the control volume and the gas Mach number Ma2 at the outlet end face 6 of the control volume, and the average friction coefficient is calculated using formula (10). Finally, the average friction coefficient is characterized by the Mach numbers of the intake end face 5 and the outlet end face 6.

[0063] Step 3: Design the size parameters of the rectangular cross-section microstructure in the downstream direction

[0064] Utilizing the vortex-shedding suppression characteristics of the streamwise microstructures, a streamwise rectangular-section microstructure 2b is designed on the inner wall surface 2a of the gas wave tube, as shown in Figure 5 、 Figure 6 . For the depth design of the microstructure 2b, the designed depth D m needs to be greater than the thickness of the viscous sublayer δ, and the thickness of the viscous sublayer δ of the gas wave tube 2 is calculated by Equation (11), δ = 0.082 mm.

[0065] If the microstructure 2b needs to effectively interfere with the coherent structure of the vortex system generated by the incident loss, the microstructure spacing S m needs to be less than 20δ, and the microstructure width W m needs to be greater than 5δ. Combining Equation (11), the calculated depth D m of the added microstructure ≥ 0.082 mm, the width W m > 0.41 mm, and the microstructure spacing S m < 1.64 mm. Rounding up, the minimum depth of the microstructure 2b is 0.1 mm. Considering that the wall thickness of the gas wave tube 2 is 1.5 mm, the thinnest thickness should be greater than 0.5 mm when the added microstructure 2b still has impact resistance. The maximum depth of the microstructure 2b can be obtained as 0.5 mm. Therefore, the available depth distribution of the microstructure is 0.1 - 0.5 mm, the maximum microstructure spacing S m is 1.64 mm, rounding down to 1.6 mm. Thus, the microstructure width W m = 0.5 - 1.6 mm. Considering that the high-pressure incident air flow generated at the intake nozzle 3 is in a one-dimensional Poiseuille-type distribution, in order to expand the vortex-shedding suppression characteristics of the microstructure 2b, the microstructure 2b needs to be arranged with a certain offset in the flow channel.

[0066] For the design of the offset angle α of the in-tube microstructure 2b, where the Reynolds number Re is 244542, A fa is the actual free-flow area in the gas wave tube 2, which is 188.15 mm 2 , and A fn takes the maximum value of 193.44 mm 2 . To prevent the added microstructure 2b from generating strong resistance increase and consumption, the range of the average friction coefficient can be restricted by combining the magnitudes of Ma1 and Ma2. Based on Equation (10) and the simulation results, the average friction coefficient is 0.013. Selecting the gas wave tube after adding the microstructure The range is [0.012, 0.05]. Substituting into Equation (12), the microstructural offset angle can be obtained as 1.5° ≤ α ≤ 9.2°. In this interval, the microstructures with offset angles have lower frictional resistance. Considering the actual feasibility of processing and to effectively interfere with the development of the main vortex system, the reasonable value range of the microstructural offset angle is 1.5° ≤ α ≤ 6°. Moreover, the larger the microstructural offset angle, the longer the action length of the microstructures and the better the drag reduction effect. Therefore, the offset angle of 6° is selected as the microstructural offset angle α = 6°.

[0067] Step Four: Take the microstructural size parameters with different depth-width ratios and conduct orthogonal comparison experiments.

[0068] Divide the microstructure depth obtained in Step Three into 5 samples equally, and also divide the microstructure width into 12 samples equally. Thus, 60 groups of microstructural size parameters with different depth-width ratios can be obtained for orthogonal simulation comparison experiments. Use 3D modeling software to establish the overall model of the hub and import it into Fluent. Extract the single-channel flow passage fluid domain and divide structured grids. According to the actual operating conditions, such as pressure inlet - pressure outlet, etc., set the boundary conditions, and select the large eddy simulation (LES) model for dynamic simulation.

[0069] Step Five: Establish an evaluation criterion for the supercharging and vortex-shedding reduction effect and obtain the optimal microstructural parameter matching conditions.

[0070] Use the Q criterion to calibrate the maximum vortex kinetic energy intensity and give the influence of the microstructural gas wave tube flow passages with different depth-width ratio size parameters on the vortex kinetic energy. Generate the orthogonal experiment comparison Table 1 according to the simulation results. The influence of each microstructural gas wave tube flow passage on the vortex kinetic energy is shown in Figure 7 .

[0071] From Table 1 and Figure 7 Analysis shows that the optimal microstructural parameter matching condition is the microstructural morphology size with a width of 1.1 mm and a depth of 0.3 mm. Calculate the kinetic energy effect η according to Equation (13). Substitute the data in the table, 0.058962 J, and the calculation result of Equation (5), 0.079 J, for calculation. It is obtained that this size parameter has the maximum supercharging and vortex-shedding reduction effect on the main vortex system kinetic energy, with η reaching 25.4%. In this gas wave hub structure, the rectangular-tooth-shaped microstructure with a width of 1.1 mm, a depth of 0.3 mm, and an offset angle of 6° has the best vortex-shedding characteristics, reducing the energy loss caused by the incident turbulent vortices.

[0072] Table 1 Comparison of the vortex-shedding reduction capabilities of microstructural tubes with different depth-width parameter combinations

[0073]

[0074] The design method of the micro-structure in the gas wave channel for pressurizing and vortex shedding can, without changing the macroscopic flow characteristics of the existing channel, add the micro-structure for pressurizing and vortex shedding on the inner wall surface of the gas wave tube, induce the momentum exchange of the near-wall vortex system / flow bundle, effectively reduce the intensity of the maximum turbulent vortex in the main flow bundle, reduce the loss of the conversion of pressure energy into vortex kinetic energy, and has practical application significance for improving the isentropic refrigeration efficiency of the rotary gas wave refrigerator.

Claims

1. A design method for microstructures in a gas wave channel that enhances pressure and eliminates vortices, characterized in that, This method first constructs a shock tube calculation model, calculates the jet loss during the high-pressure jet stage of the flow channel, analyzes the origin of turbulent vortices at the leading edge of the flow channel during the intake process, and characterizes the average friction coefficient of the shock tube inner wall. Secondly, based on the passive control theory of wall turbulence, considering the thickness of the viscous sublayer of the flow channel and the actual flow area of the flow channel, the optimization interval of the micro-structure size of the pipe wall is determined. Then, orthogonal simulation comparison is carried out to analyze the specific influence of the micro-structure morphology with different depth-width ratios on turbulent vortices. Finally, an evaluation criterion for the supercharging and vortex-suppressing effect is established, and the optimal micro-structure size parameters for supercharging and vortex-suppressing are obtained according to the criterion. The specific steps of the method are as follows: Step 1: Construct a calculation model for the flow characteristics of the shock tube a) Calculate the equivalent diameter d of the gas wave tube t Based on the analysis of the fluid flow state in the gas wave tube, first simplify the gas wave tube (2) in the rotating hub (1) into a one-dimensional gas wave tube, and assume the width of the flow channel in the gas wave tube is W t , the chord length of the bottom arc surface is L t , the angle occupied by the axial arrangement is α t , therefore, the cross-sectional area A of the gas wave tube t is: Wetted perimeter χ t is as follows: Taking the cross-sectional area A of the water flowing through the quadruple pipe t and the wetted perimeter χ of the pipe cross-section t as the equivalent diameter d of the simplified gas wave tube t : b) Mathematically describe the intake nozzle of the shock tube, and calculate the turbulent kinetic energy generated by jet loss and the jet loss during the gradually opening and closing stage The high-pressure outlet nozzle (4) is a constant-pressure outlet end; simplify the velocity distribution of the high-pressure intake nozzle (3), ignore the body force of the gas in the flow channel, and the velocity distribution at the nozzle is a one-dimensional Poiseuille type: Among them, v1 is the velocity of the intake nozzle, μ is the air dynamic viscosity coefficient in this state, k1 is the proportional correction coefficient of the nozzle velocity, which needs to be corrected according to the actual measurement experiment results, D is the nozzle diameter, and y is the vertical distance from a point in the nozzle to the lower wall of the pipe; Let h j be the turbulent kinetic energy of the shock tube, which is obtained by formulating the kinetic energy equation based on the velocity difference between the high-pressure intake nozzle (3) and the high-pressure outlet nozzle (4): Among them, k2 is the proportional correction coefficient of turbulent kinetic energy loss, g is the local acceleration of gravity, v2 is the flow velocity at the air outlet nozzle, A1 is the relative cross-sectional area when the nozzle and the flow channel start to diverge, A2 is the cross-sectional area of the pipeline through which water flows, that is, A t ; The turbulent kinetic energy generated due to jet loss is calculated using formula (5) to describe the magnitude of jet loss in the stage of gradual opening and closing. This part of the loss is manifested in the form of turbulent vortices. If the turbulent kinetic energy loss is greater, the size and vortex kinetic energy of the turbulent vortices are greater; Step 2: Characterize the average friction coefficient of the shock tube inner wall Analyze a control volume (7) with a length of dx in the leading edge of a one-dimensional gas wave tube with an axial length of L. Assume that the tangential stress of the wall on the gas is τ w , the critical speed of sound is c cr , γ is the adiabatic coefficient of air in this state; assume that the cross-sectional velocity coefficient in the control volume (7) is M * = v / c cr , Ma is the fluid Mach number at the cross-section in the control volume (7), v is the fluid flow velocity at the cross-section in the control volume (7), and: Define the friction resistance coefficient of the inner wall of the pipe as C f , τ w is the tangential stress of the wall on the gas, ρ is the density of air in this state, υ is the specific volume of air, then the friction resistance coefficient of the inner wall of the pipe is: List the momentum equation for the control volume (7) and integrate to obtain: where M *1 is the cross-sectional velocity coefficient at the intake end face (5), and M *2 is the cross-sectional velocity coefficient at the intake end face (6). Therefore: Use formula (6) to replace M with Ma 2 Replace M * 2 , set the gas Mach number Ma1 at the intake end face (5) of the control volume and the gas Mach number Ma2 at the outlet end face (6) of the control volume, and the average friction drag coefficient The calculation formula is as follows: Finally, the average friction coefficient was characterized by the Mach numbers of the intake end face (5) and the exhaust end face (6). Step 3: Design the size parameters of the micro-structure with a rectangular cross-section in the flow direction Utilize the vortex-suppressing characteristics of the micro-structure in the flow direction to design a micro-structure (2b) with a rectangular cross-section in the flow direction on the inner wall surface (2a) of the shock tube; the constraint conditions for the micro-structure size are: 1) Design depth D m It is required to be greater than the thickness δ of the viscous sublayer. Calculate the thickness δ of the viscous sublayer of the gas wave tube: 2) If the rectangular cross-section microstructures (2b) in the downstream direction need to effectively interfere with the coherent structure of the vortex system generated by the incident loss, the microstructure spacing S m shall be less than 20δ, and the microstructure width W m shall be greater than 5δ. At the same time, the inner wall perimeter of the gas wave tube (2) is χ t , and the number of microstructures is jointly determined according to the above conditions and the actual situation; 3) Considering that the high-pressure incident air flow generated at the high-pressure intake nozzle (3) is a one-dimensional Poiseuille type distribution, in order to expand the vortex-suppressing characteristics of the micro-structure (2b) with a rectangular cross-section in the flow direction, it is necessary to arrange the micro-structure (2b) with a rectangular cross-section in the flow direction in the flow channel at a certain offset angle α. The calculation method for the offset angle α is: where Re is the Reynolds number of the gas in the flow channel, A fa is the actual free flow area in the gas wave tube (2), i.e., A t , A fn is the nominal flow area based on the inner diameter of the tube after adding the microstructures, which is the free flow area plus the increased area after adding the microstructures; Combined with the above conditions and formulas, obtain the specific design parameter ranges for the depth, spacing, width, offset angle, and number of the micro-structure; Step 4: Select the size parameters of the micro-structure with different depth-width combinations and conduct orthogonal comparison experiments; Select M groups of size parameters with different depth-width combinations from the micro-structure size range calculated above for orthogonal simulation comparison experiments; use 3D modeling software to establish the overall model of the impeller and import it into Fluent, extract the fluid domain of a single-channel flow channel, divide structured grids, and select the large eddy simulation (LES) model for dynamic simulation according to the actual operating conditions, i.e., design boundary conditions such as pressure inlet - pressure outlet; Step 5: Establish an evaluation criterion for the supercharging and vortex-suppressing effect and obtain the optimal micro-structure parameter combination conditions; Calibrate the maximum vorticity kinetic energy intensity with the Q criterion, and give the influence of the micro-structured gas wave tube flow channels with different depth-width matching size parameters on the vorticity kinetic energy; use the ratio of the maximum eddy viscosity intensity Ω Max to the maximum eddy viscosity intensity Ω Max' of the micro-structured flow channel as the evaluation criterion, and establish an evaluation method for the supercharging and vorticity reduction effect, that is: Finally, according to the comparison results of the orthogonal simulation experiments, obtain the size parameters of the micro-groove depth-width combination with the best supercharging and vortex-suppressing effect.

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