KR100346911B1 - Axial-flow fan bladedesigned by low noise fan design method - Google Patents

Abstract

The present invention relates to a method for designing an axial fan using a numerical optimum design, and in particular, after setting an arbitrary blade as an initial shape of an optimal design, a design function corresponding to a target function according to a target value to be changed and limitations required for design Process to define the flow rate, to form a lattice system for three-dimensional spatial coordinates to analyze the flow field, and to perform three-dimensional flow analysis in the flow field rotating at an angular velocity of Ω about the x-axis using a finite volume method. The process of determining the search direction for the design variables using the gradient method, and performing the one-dimensional search according to the determined search direction to calculate the optimal distance in the determined search direction and changing the design variables accordingly to change the objective function And determining whether or not the design data calculated accordingly is suitable. It provides a fan design method comprising the step of recalculating the system and performing design changes again, and low noise axial fan blades designed according to the method, and large-scale implementation of the design method according to the existing theoretical and empirical formulas. You can design the optimal type of axial fan to meet your design specifications without error.

Description

Axial-flow fan blade designed by low noise fan design method

The present invention relates to a method for designing a cooling fan used to suppress heat generation of various electronic devices or mechanical devices, and more particularly, to a simulation design method for a cooling fan which is a main component of an automotive air conditioning system and an engine cooling system. will be.

In general, the mounting trend of the DOHC engine is accelerating to improve ride comfort and driving performance due to the rapid development and growth of the domestic automobile industry.

Therefore, there is an urgent need to improve the engine cooling performance by installing DOHC engines and to increase the high pressure due to the application of a new refrigerant air-conditioning system. As a solution, high efficiency of the fans is required and low noise fans are required. It is necessary to improve the fan design technology.

However, studies to improve the design and efficiency of axial fans up to now have been mostly to predict the deterioration and efficiency by approximate integral analysis. This approximate design method establishes the design conditions and predicts the design result by the speed triangle at the entrance and exit of the wing, and the momentum equation and the energy equation in the middle plane of the average wing height and the two wings in one or two dimensions. This method does not reflect complex flow structures such as vortex and secondary flow generated inside the fan, and requires many empirical formulas to compensate for this, and requires a lot of empirical elements of the designer. In order to design a large number of trial and error occurs due to the lack of empirical formula.

However, the performance of the fan depends on the geometry of the wing, so the design of complex three-dimensional curved surfaces cannot be successfully achieved without considering three-dimensional flow phenomena such as secondary flow or separation of flow due to more accurate hydrodynamic flow analysis. In addition, the design method described above is difficult to establish accurate design technology, and design of the field where the experimental research is insufficient requires very much time and economic loss.

Therefore, in order to overcome the limitations of the prior art according to the above-described approximate integral type analysis, the proposed technique is a design method combining a flow analysis technique based on computational fluid dynamics and an optimal design technique.

Among the optimal design methods, the optimal design techniques that have been used for the design of the aircraft airfoil geometrically similar to the axial fan blades are largely classified into an inverse design method and a numerical optimization method.

Among these methods, the reverse design method is used only for simple airfoil shape and complicated shape because it is a method of determining the ideal flow characteristics, that is, the pressure or velocity distribution on the wall and obtaining the shape of the object. The design method of the three-dimensional fan blade has a disadvantage that it is difficult to apply a lot of inappropriate parts.

However, the numerical optimal design method can determine the function to be minimized or maximized and find the design variables that can be satisfied without knowing the information about the optimal design point in advance, and it has automatic design ability, insert various constraints, fluid flow and heat transfer. This has the advantage that it can be applied to various engineering fields, but on the other hand, it takes a lot of calculation time due to the repetitive flow analysis, and furthermore, the current research process shows that the Euler equation or two-dimensional non-viscosity equation In many cases, analysis by boundary layer equations is used, which causes the problem of not properly reflecting the phenomena of real flow when the numerical optimal design method is applied.

Therefore, it is difficult to meet the consumer's demand for high efficiency and low noise of the fan in the existing approximate design method and the optimal design method using the non-viscosity equation or the two-dimensional equation as the flow analysis means. Moreover, these designs use foreign technology, causing a considerable increase in production costs.

An object of the present invention for solving the above-mentioned problems of the prior art is a function of reducing noise as flow information by simulation of a precise three-dimensional Navier-Stokes equation that can accurately analyze the flow structure of a cooling axial fan. The purpose of this study is to provide a design method by numerical optimum design method for low noise. This design technique using this three-dimensional flow simulation as a direct fan design means is the first attempted in Korea and abroad.

1 is an exemplary operation sequence for explaining the fan design method according to the present invention

2a and 2b is a front view and side view of the fan blade input before the optimum design

3 is a diagram illustrating a change process of design variables

4 is a view illustrating a change process of the objective function

5a to 5c is a comparison of the existing fan blades and the optimum fan blades and front and side views of the optimum fan

6 is a graph comparing the noise measurement of the existing fan and the optimum fan

A feature of the present invention for achieving the above object is, in the axial fan design method using a numerical optimum design, the first process of setting the wing surface coordinates for the three-dimensional shape of the fan currently being produced as the initial shape of the optimum design and And a second process of selecting an objective function according to a target value to be changed in the initial shape set through the first process and setting a corresponding geometric or hydrodynamic variable as a design variable, and through the second process. When a function and a design variable are set, a third process of defining a constraint such as limiting a range of geometric and hydrodynamic variables including the design variable or maintaining a specific value, and after the third process is performed, To construct a flow field that rotates at an angular velocity of Ω about the x-axis with respect to the three-dimensional spatial coordinates to solve the desired flow field. A fourth process of forming a magnetic field, a fifth process of performing a flow analysis by discretizing a three-dimensional Navier-Stokes equation using a finite volume method, and a search direction for design variables using a compound gradient method. A sixth process and a seventh process of performing an one-dimensional search according to the search direction determined through the sixth process to calculate an optimal distance in the determined search direction and changing the design variable accordingly to change the objective function; Whether the design data obtained according to the set design variable, the objective function and the constraint condition is suitable for the design data changed through the fourth to seventh steps is suitable or the design range of the gradient vector does not change or the value of the objective function or the design variable. The eighth step of determining whether the error is within the predetermined relative error, and if it is determined to be suitable through the eighth step, ends the numerical optimum design and is appropriate. If determined that the paper has to include a ninth step of performing a design change material proceeds to the fourth step.

Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings.

First, looking at the concept of the mathematical theory used in the present invention, the general expression of the optimization problem in the numerical optimization design method is shown in Equation 1 below.

Here, the variable x is a vector of design variables, and the superscripts l and u represent the lower limit and the upper limit of each design variable. The optimization algorithm is performed through an iterative process by changing the design variables as shown in the following equation.

x ^ q ~ = ~ x ^ q-1 ~ + ~ α_q ^ * ~ d ^ q ~

Where q is the number of repetitions, x is a vector of design variables, d ^q is the search direction and α _q ^* is the moving distance in the search direction as in Equation 1.

In this case, a gradient or gradient vector that is frequently used to determine the search direction is defined as in Equation 3 below.

Since the gradient vector defined as shown in Equation 3 appears in the direction of the maximum rate of change of the function f, the method of minimizing the objective function using this property is to change the design variable in the opposite direction of the gradient vector. There is a descent method and a compound gradient method using information about the search direction in the previous calculation.

In the case of applying the double compound gradient method, the search direction is defined as in Equation 4 below.

Above, we have briefly reviewed the numerical optimal design method, and the sequential unconstrained minimization technique (SUMT) using penalty function is easy to solve the complex problem in tracking optimal variables of optimization problems with constraints. In addition, the sequential ratio limit minimization technique is applied, that is, a new objective function is added to the objective function in the numerical optimal design method. The new objective function is defined as in Equation 5 below.

In this equation, r _p is a penalty variable, ε is a transition parameter, and C is a constant.

In addition, the present invention obtains numerical solutions to the continuous equations and momentum equations for incompressible three-dimensional steady flow in order to obtain the objective function and its derivatives in the flow through the rotating axial fan. Has the same form as

In Equation 6, x, y, z represent rotational coordinates that rotate at an angular velocity of Ω about the x-axis. In addition, centrifugal acceleration and Coriolis acceleration according to the rotation of the coordinate system are included in R.

The reason why the Navier-Stokes equation is used for the design of the fan is that the Navier-Stokes equation can be used to analyze the flow field through the Navier-Stokes equation. This is because significant accuracy and effectiveness can be achieved without using an empirical or empirical element. This accurate information can be passed directly to the numerical optimal design algorithm to obtain the optimal shape.

In addition, in the present invention, the finite volume method (FVM) is used to discretize the governing equations transformed into the non-orthogonal curve coordinate system, and for this purpose, the momentum equation is converted into an extended governing equation for 3D problems. In this process, linear upwind differencing scheme is used for convective terms and central-difference approximation is used for diffusion terms.

Therefore, in the present invention, a Strongly Implicit Procedure (SIP) was used to solve the discretized logarithm of the differential equation, and the SIMPLEC method was used as the speed-pressure correction algorithm. For the analysis of turbulent flow, standard k-ε and k-ω models were used as models according to the Navier-Stokes equation.

In addition, the boundary of the computational domain of the flow was divided into an inlet boundary, an outlet boundary, a wall boundary, and a periodic boundary.

Since the regeneration of the grid system due to the continuous shape change should be repeated effectively, it is preferable to adopt the logarithmic grid generation method rather than the excessively time-dependent differential grid generation method. Used.

As design variables, variables related to the sweep angle (γ) representing the degree of warpage of the fan blades were selected. When the distribution of the sweep angle is expressed as a quadratic function, the first design variable is the sweep angle at the average wing height, and the second design variable is the sweep angle at the tip of the wing, which corresponds to the maximum sweep angle, which is expressed as an equation. If it can be defined as shown in Equation 7 below.

The mathematical theory for the optimal design of axial fan by mathematical arithmetic was examined. Therefore, the fan design method according to the present invention for the optimal design of the axial fan by applying the above arithmetic theory will be described.

1 is a flow chart for explaining a fan design method according to the present invention, although not shown, the design method according to the present invention is capable of designing a variety of fluid machines, and in addition to the three-dimensional shape drawings, various three-dimensional speed, pressure, turbulence, etc. It provides data support for the graphics processing of information and can be run on workstations and personal computers.

First, looking at the flow of the technical ideas to be applied in the present invention step by step, the shape implementation step of the initial fan, the definition step of the design variable, the definition step of the objective function, the step of giving constraints, the generation step of the grid system, the three-dimensional flow The analysis step, the determination of the search direction, the one-dimensional search in the search direction, the determination of the convergence condition, and the design change step are performed in this order.

Therefore, briefly describing each of the above-described steps, the shape implementation step of the initial fan implements the initial shape for the model that is the object of optimal design. This initial shape changes its shape according to the adopted design variables. When the existing model is set as the initial shape, the performance of the existing model is improved in the desired direction. Also, if only the design conditions are given as the initial shape, one or two dimensions are given. The initial shape is implemented through design and quasi-three-dimensional design and used as the initial shape of the optimal design.

In addition, the step of defining design variables sets the geometric or hydrodynamic variables to be changed in the initial shape as design variables.

In addition, the definition of the objective function can be referred to as the design goal. The optimal design algorithm changes the design to minimize or maximize the value of the objective function. For example, pressure coefficients, flow coefficients, and efficiency can be selected as objective functions. In this study, new objective functions were developed to reduce noise and increase air volume. This objective function must be physically valid so that the designer can automate the design in the desired direction.

In addition, the step of granting the constraints may impose constraints such as limiting the range of geometrical and hydrodynamic variables including design variables or maintaining a specific value.

In addition, the generating step of the lattice system is a pretreatment process for analyzing the desired flow field to generate a lattice system for determining the calculation point in the flow field.

In addition, the three-dimensional flow analysis step uses the finite volume method to perform the flow analysis in the flow field and provides information for the objective function or sensitivity analysis required by the optimal design algorithm. This three-dimensional flow analysis is an important part of determining the quality of optimal design results. As a result of the literature review, there is no example of using the three-dimensional analysis of viscous flow in the optimum design, and the attempt in the present invention enables a very good design.

In addition, the step of determining the search direction determines the search direction for the design variables by using a conjugate gradient method, and by changing the design variable in this direction, the value of the objective function can be improved.

Further, in the one-dimensional search step in the search direction, the optimum distance in this direction is determined when the search direction is determined. Once this optimal distance is found, the variable obtained here has the improved value of the objective function compared to the previous step.

The convergence condition of the numerical optimum design is that the convergence condition of the numerical optimal design is defined as the design range in which the value of the gradient vector does not change or when the value of the objective function or design variable is within a constant relative error. I think that.

In addition, the design change step finds an optimal variable as the search direction and the moving distance in the search direction. Create the grid system again based on the shape defined as this variable and repeat the above method until the convergence condition is satisfied.

The flow of the technical idea described above is illustrated in the accompanying FIG. 1. Referring to the operation sequence shown in the attached FIG. 1, in step S101, the shape of the initial fan, that is, the object of the optimal design is determined. Implement the initial shape for the model. This initial shape sets the wing surface coordinates of the three-dimensional shape of the existing axial fan as the initial shape of the optimal design. The shape is changed by the design variables adopted. If the design condition is given as the initial shape, and the design condition is given as the initial shape, the initial shape is implemented through the one-dimensional design and the two-dimensional aerodynamic design and used as the initial shape of the optimum design.

Thereafter, in step S102, design variables are defined, and geometric or hydrodynamic variables to be changed in the initial shape are set as design variables. In addition, in step S103, an objective function is defined. In this case, the objective function is set as shown in Equation 5, and the optimal design algorithm changes the design in a direction that minimizes or maximizes the value of the objective function. For example, the pressure coefficient, flow coefficient, efficiency or ratio of turbulent kinetic energy and pressure head as in the present invention may be selected as the objective function.

As described above, when the design variable and the objective function are set through the process of step S102 and step S103, in step S104 to limit the range of the geometrical and hydrodynamic variables including the design variable or to maintain a specific value, etc. This part reflects the various requirements of the designer in the numerical optimal design algorithm and guarantees the numerical stability, and the result of the structural analysis can be inserted in this part and reflected in the optimal design.

Thereafter, in step S105, a lattice system is generated. The lattice system generates a lattice system according to Equation 6 above to determine a calculation point in the flow field as a preprocessing process for analyzing a desired flow field.

After generating the lattice system through the process of step S105, the flow proceeds to step S106 to perform the three-dimensional flow analysis, which performs the flow analysis in the flow field using the finite volume method, and the objective function or sensitivity required by the optimal design algorithm. Provide information for interpretation.

Thereafter, the process of step S107 determines the search direction for the design variables by using the compound gradient method according to Equation 4, and proceeds to step S108. At this time, if the design variable is changed by the search direction determined in step S107, the value of the objective function can be improved.

In step S108, a one-dimensional search is performed according to the search direction determined in step S107, that is, an optimum distance in the determined search direction is calculated. The optimal distance calculated through this process has the value of the improved objective function compared to the previous stage variable.

In step S109, it is determined whether the design value obtained according to the predetermined design variable, the objective function, and the constraint condition through the process of steps S105 to S108 described above is suitable for the convergence condition. This is a design range where the gradient vector does not change as a convergence condition of the digital optimum design, or when the value of the objective function or design variable is within a certain relative error, and the like is determined to be the best design.

At this time, if it is determined in step S109 that the currently designed values are unsuitable for the convergence condition, the process proceeds to step S110 to the design change mode and then to step S105.

Therefore, the fan's shape deformation, derivable effects and comparative experiments according to the optimum design when designing the fan according to this algorithm will be described with reference to the accompanying drawings.

2a and 2b is a front view and a side view of the fan blade input before the optimum design, Figure 3 is an illustration of the process of changing the design parameters, Figure 4 is an illustration of the process of changing the objective function, Figures 5a to 5c A comparison of the existing fan blades with the optimum fan blades and a front view and a side view of the optimum fan, Figure 6 is a graph comparing the noise measurement of the existing fan and the optimum fan.

Front and side views of the fan blades shown in Figures 2a and 2b is a conventionally produced product, after setting the purpose of the optimum design to reduce the noise to the following examples of design changes to achieve the purpose of noise reduction do.

Therefore, in order to reduce noise, the present invention has developed an objective function as shown in Equation (8).

At this time, the pressure head (H) is the amount of increase in the pressure at the outlet portion based on the fan inlet portion, which is described by a simple equation in the existing design method, but because it is very inaccurate, in the present invention three-dimensional at hundreds of thousands to millions of grid points The exact value is calculated using the flow analysis technique which simulates the Navier-Stokes equation by the finite volume method. The turbulent kinetic energy generation rate (G) is also the value obtained by calculating the turbulent term in the flow analysis and integrating it throughout the flow field.

In the above description, all geometric elements are possible as design variables, but the following description is defined as a function related to the sweep angle of the wing.

Therefore, the design variable defined as a function related to the sweep angle of the blade is changed as shown in FIG. 3, and the objective defined by Equation 8 as the design variable is changed as shown in FIG. The calculated value of the function is changed from 107.9 to 89.6 as shown in FIG.

3, the sweep angle in the initial shape is 0 ^o, but the sweep angle in the final design stage obtained through the optimal design method developed in the present invention is -3.86 ^o at the average wing height and the tip of the wing. Is 9.93 ^o . Therefore, defining the hub and the average blade height, and the radial sweep of the axial fan blades, using the three sweep angle of the wing tip to the boundary conditions of Equation (7) distribution of the _{γ (r n) γ (r} n) = 35.3r _n ² -25.37r _n . R _n means a dimensionless radius, and is defined as r _n = (rr _h ) / (r _t -r _h ), where r _t is the tip radius, r _h is the hub radius, and r Is the radial distance from the axial center of the axial fan to any position. And the tip (tip) means the end of the wing which is located farthest from the axis center, tip radius (r _t ) means the distance from the axis center to the tip. The average wing height r _m is a radius that divides the flow path area into two when the hub radius is r _{h and the} tip radius is r _t , such as r _m = ((r _t ² + r _h ² ) / 2) ^0.5 As shown in Fig. 5B, the sweep angle γ (r _n ) represents the degree to which the fan blades bend in the rotational direction as an angle, and the sweep angle at a given radial position r means the fan. The direction of rotation between the cord and fan centers at the hub and blade boundary of the blade and the line passing through the cord and fan centers of the blade at a given radial position (r). The side is defined as (+) and the reverse direction is defined as (-).

Accordingly, the shape of the existing fan blades indicated by dotted lines in FIG. 5A is changed to the blade shape of the optimally designed fan indicated by solid lines. 5B and 5C are front and side views of an optimally designed fan.

As shown in FIG. 6, the result of performing the noise measurement (measurement position: 1m forward from the center of the fan) after applying the same motor rotation as that of the existing fan after fabricating the optimally designed fan as described above. The noise of the existing axial fan is 71dB (A), whereas the optimum design of the axial fan is 66.5dB (A), and the noise reduction is about 4.5dB (A). Accordingly, it can be seen that the noise is greatly reduced.

As described above, by providing a fan design method according to the present invention, it is possible to break away from the approximate design method based on the existing theoretical and experimental formulas, and to use mathematics, hydrodynamics, and fluid mechanical theory organically. By analyzing, it is possible to design an axial fan with an optimal shape effectively.

Therefore, in the conventional method of numerical optimization design, since the flow information of the non-viscosity equations such as the two-dimensional Euler equation is used, the flow phenomenon of the complex blower cannot be reflected in the design, but in the present invention, the three-dimensional Navier-Stokes equation is applied. As a result, it is possible to predict not only the influence of viscosity but also very complicated flow phenomenon through simulation, so the design accuracy is very high. An example of directly reflecting this three-dimensional viscous flow analysis in numerical optimal design has not been published worldwide. In addition, the conventional method merely aims to improve efficiency, static pressure, etc., but in the present invention, the ratio of turbulent kinetic energy and pressure head as a function of predicting the noise was able to effectively reduce the noise of the blower.

Claims (3)

When the hub radius is r _h , the tip radius is r _t , and r _n is (rr _h ) / (r _t -r _h ), the radial sweep angle γ (r _n ) of the axial fan blade is γ (r _n ) = 35.3 r _n ² -25.37 r _n A low noise axial fan blade characterized in that it has a distribution. The sweep angle γ _m at the average wing height of the axial fan blade is -4.36 ° ≤ γ _m ≤-3.36 °, and the sweep angle γ _t at the tip is 9.43 ° ≤ γ _t A low noise axial fan blade, characterized in that ≤10.43 °. The low noise as claimed in claim 1, wherein the sweep angle γ _m at the average wing height of the axial fan blade is -3.86 ° and the sweep angle γ _t at the tip is 9.93 °. Axial fan wings.