Method for calculating flow characteristics of two-phase flow of lubricating oil and air in high-speed contra-rotating ring cavity

Abstract

The invention discloses a flow characteristic calculation method for lubricating oil and air two-phase flow in a high-speed contra-rotating ring cavity. The flow characteristic calculation method comprises the following steps: determining assumed conditions of an inter-shaft flow model of a contra-rotating shaft cavity with a wall surface oil film; establishing air velocity distribution in an annular cavity, and determining a shear stress expression of the outer wall surface of the low-pressure shaft and an oil-gas interface; wall surface oil film speed distribution is established, and an oil-gas interface viscous shear stress expression is determined; solving an unknown quantity of the velocity distribution model of the lubricating oil-air two-phase flow in the rotating ring cavity; determining boundary conditions for the velocity distribution model of the lubricating oil-air two-phase flow in the annular cavity; a tangential speed distribution model in the contra-rotating ring cavity with the wall surface oil film is obtained and used for achieving calculation of the flowing characteristics of the lubricating oil and air two-phase flow in the high-speed contra-rotating ring cavity. According to the technical scheme, the speed distribution expression in an analytical form is defined, and a simple and effective method is provided for calculating the flow characteristics of the two-phase flow in the counter rotating ring cavity.

Description

Technical Field

[0001] The invention relates to the field of aeroengine design, and in particular to a method for calculating flow characteristics of a lubricating oil-air two-phase flow in a high-speed counter-rotating annular cavity. Background Art

[0002] As the DN value (the product of the inner diameter of the bearing (mm) and the shaft speed (r / min)) of aircraft engine main bearings continues to increase, the requirements for the operating environment of the engine main bearings are also increasing. In order to ensure the optimal lubricating oil supply to the engine main bearings and normal operation, it is necessary to use injection lubrication and under-ring lubrication to ensure the normal operation of the engine main bearings. The under-ring lubrication structure consists of an oil collecting part and an oil delivery part. The oil collecting part includes an oil collecting structure, a nozzle, etc. The oil delivery part includes a radial oil supply hole on the bearing and an inner sleeve with an axial groove; the oil collecting structure is located between the high-speed counter-rotating high-pressure and low-pressure rotor shafts. The lubricating oil and air flow in the annular cavity between the high-speed counter-rotating shafts are complicated. It is difficult to establish a flow and heat exchange test platform between dual rotating shafts based on similar principles.

[0003] At present, the analysis of the flow characteristics of the oil-air two-phase flow in the swivel cavity of an aircraft engine mainly focuses on the CFD numerical simulation method. There are few theoretical analyses of the two-phase flow in the swivel cavity based on flow phenomena, and there is a certain degree of difficulty in calculating the flow characteristics of the two-phase flow. Summary of the invention

[0004] In order to solve the above problems, the present application provides a method for calculating the flow characteristics of the lubricating oil-air two-phase flow in a high-speed counter-rotating annular cavity, which is characterized by comprising the following steps:

[0005] Determine the assumptions of the interaxial flow model of the counter-rotating shaft cavity with the presence of wall oil film, wherein the assumptions are used for the oil-air two-phase flow under stable working conditions;

[0006] Establish the air velocity distribution in the annular cavity and determine the shear stress expression at the outer wall of the low-pressure shaft and the oil-gas interface;

[0007] Establish the wall oil film velocity distribution and determine the expression of viscous shear stress at the oil-gas interface;

[0008] According to the shear stress expressions at the outer wall of the low-pressure shaft and the oil-gas interface and the viscous shear stress expression at the oil-gas interface, the unknown quantities of the velocity distribution model of the lubricating oil-air two-phase flow in the counter-rotating annular cavity are calculated;

[0009] Determining boundary conditions for the velocity distribution model of the lubricating oil-air two-phase flow in the annular cavity;

[0010] A tangential velocity distribution model in a counter-rotating annular cavity with a wall oil film is obtained, and the tangential velocity distribution model in the counter-rotating annular cavity is used to calculate the flow characteristics of the lubricating oil-air two-phase flow in a high-speed counter-rotating annular cavity.

[0011] Among them, the expressions for determining the shear stress at the outer wall of the low-pressure shaft and the oil-gas interface include:

[0012] Based on the experimental correlation between the velocity distribution structure of the Karman three-layer of the flat plate turbulent boundary layer and the rotating shaft torque coefficient, the low-pressure rotor shaft torque coefficient C is determined. m1 ;

[0013] Introducing the correction coefficient affected by Taylor vortex, the shear stress expression at the outer wall of the low-pressure axis is determined

[0014] Based on the condition that the shear stress at the oil-gas interface and the outer wall of the low-pressure shaft produce the same torque, the shear stress expression τ at the oil-gas interface is determined. oil,air , expressed as:

[0015] Among them, ω1 is the angular velocity of the low-pressure shaft, ω2 is the angular velocity of the oil-gas interface, and ρ air is the air density, C m1 is the torque coefficient of the low-pressure rotor shaft, R1 and R2 are the outer diameter of the low-pressure shaft and the radius of the oil-gas interface from the rotation axis, respectively, and Re1 is the Reynolds number of the low-pressure shaft rotation.

[0016] Among them, the expression for determining the viscous shear stress at the oil-gas interface includes:

[0017] Establish the relationship between the velocity distribution of the oil film on the wall;

[0018] Obtain the initial conditions for calculating the wall oil film velocity distribution relationship, including: high and low pressure rotor rotation angular velocity ω3, ω1, high and low pressure shaft radius R3, R1, oil film thickness range δ oil , where the wall oil film thickness δ oil Based on the numerical calculation of the oil collecting structure of the counter-rotating annular cavity;

[0019] Determine the boundary conditions for calculating the wall oil film velocity distribution relationship, including: the tangential velocity of the oil-gas interface ω2R2, the high-pressure rotor shaft wall velocity ω3R3;

[0020] Define the expression of viscous shear force at the oil-gas interface It is expressed as:

[0021]

[0022] Among them, δ oil is the thickness range of the lubricating oil film layer, and: oil =R3-R2, μoil is the dynamic viscosity of lubricating oil.

[0023] Before obtaining the initial conditions for calculating the wall oil film velocity distribution relationship, the thickness range δ of the lubricating oil film layer is obtained by rotating the annular cavity oil collecting structure geometric model. oil ,include:

[0024] Establish the geometric model of the counter-rotating annular cavity oil collecting structure;

[0025] Perform regional discretization;

[0026] Based on the VOF method and sliding network technology, the solver parameters are set to perform unsteady-state solutions;

[0027] Obtain the distribution of lubricating oil and air volume fractions and the thickness of lubricating oil film at different circumferential cross sections;

[0028] Extract the radial tangential velocity distribution in the annular cavity and identify the mixed interface position between the lubricating oil film layer and the air layer;

[0029] Get the thickness range of the lubricating oil film layer δ oil .

[0030] Furthermore, when establishing the velocity distribution relationship of the wall oil film, based on the Couette flow between the two rotating shafts, it is determined that the radial and axial flows are not considered under stable conditions, and the continuity equation, radial and tangential momentum equations are obtained, which are expressed as:

[0031]

[0032] Furthermore, the tangential velocity distribution model in the counter-rotating annular cavity with the wall oil film includes the tangential velocity distribution in the radial direction of the outer wall of the low-pressure shaft, the tangential velocity distribution in the radial direction of the oil-gas interface, and the wall oil film velocity distribution.

[0033] Among them, the velocity distribution of the wall oil film is expressed as:

[0034] Where r is the radius of any position in the wall oil film from the rotation axis, C oil,1 is a constant, C oil,2 is a constant, which is related to ω2, ω3, R2, and R3, where ω3 is the angular velocity of the high-pressure shaft, and R3 is the inner diameter of the high-pressure shaft, and:

[0035] The tangential velocity distribution in the radial direction of the outer wall of the low-pressure shaft is expressed as:

[0036]

[0037] The tangential velocity distribution in the radial direction of the oil-gas interface is expressed as:

[0038]

[0039] Among them, A, B, and D are constants related to the rotating Reynolds number, and C and E are constants determined by numerical calculation of the oil-air two-phase flow in the counter-rotating annular cavity. are the friction speeds respectively.

[0040] The present invention combines CFD numerical simulation, rotational flow test correlation and Karman three-layer structure velocity distribution to establish a theoretical model of lubricating oil and air flow in a counter-rotating annular cavity with a lubricating oil film layer attached, providing a calculation method for studying the flow characteristics in a high-speed counter-rotating annular cavity. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a diagram of the calculation steps of the flow characteristics of the lubricating oil-air two-phase flow in the high-speed counter-rotating ring cavity provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The present invention provides a method for calculating the flow characteristics of the lubricating oil-air two-phase flow in the high-speed counter-rotating annular cavity of an aircraft engine. Subsequently, a heat transfer process calculation model can be introduced based on the analogy theory, and the thermal boundary conditions of the annular cavity wall with an oil film interface attached are provided for the numerical calculation of the bearing-oil collecting structure using the under-ring lubrication method. It is used to analyze the influence of the thermal deformation between the rolling bearing and the journal on the inter-shaft matching properties, and can be used for calculating the flow characteristics of the lubricating oil-air two-phase flow in the high-speed counter-rotating annular cavity. The specific implementation process is as follows Figure 1 As shown, the following steps are included:

[0043] Step S100: determining the assumption of the inter-axial flow model of the counter-rotating shaft cavity with the wall oil film, the assumption is used to determine the single-phase flow state in the lubricating oil film for the lubricating oil-air two-phase flow under stable working conditions;

[0044] This step mainly ignores the dissolution effect of air in the lubricating oil film, determines the single-phase flow state in the lubricating oil film, ignores the movement trajectory of oil droplets in the air layer, and only considers the lubricating oil-air two-phase flow under stable working conditions; at the same time, the environment for calculating the flow characteristics of the present invention is determined as: the inner wall of the high-pressure shaft, the oil-gas interface and the outer wall of the low-pressure shaft.

[0045] Step S111: Establish the air velocity distribution in the annular cavity and determine the shear stress expression at the outer wall of the low-pressure shaft and the oil-gas interface;

[0046] Specific content includes:

[0047] Establish the air velocity distribution in the annular cavity: Based on the Karman three-layer velocity distribution structure of the flat plate turbulent boundary layer and the experimental correlation formula of the rotating shaft torque coefficient, determine the low-pressure rotor shaft torque coefficient C m1, expressed as:

[0048]

[0049] Among them, C m1 is the torque coefficient of the low-pressure rotor shaft, R1 and R2 are the outer diameter of the low-pressure shaft and the radius of the oil-gas interface from the rotation axis, respectively, and Re1 is the Reynolds number of the low-pressure shaft rotation;

[0050] The correction factor ε for the influence of Taylor vortex is introduced as 0.6273+4.5×10 -5 Ta1, determine the shear stress expression at the outer wall of the low-pressure shaft It is expressed as:

[0051] Among them, ω1 is the angular velocity of the low-pressure shaft, ω2 is the angular velocity of the oil-gas interface, and ρ air is the air density;

[0052] On this basis, based on the condition that the shear stress at the oil-gas interface and the outer wall of the low-pressure shaft produce the same torque, the shear stress expression τ at the oil-gas interface is determined oil,air , expressed as:

[0053] Step S112: establishing the wall oil film velocity distribution and determining the viscous shear stress expression of the oil-gas interface;

[0054] The specific steps include:

[0055] Establish the relationship of wall oil film velocity distribution: In this step, based on the Couette flow between the two rotating axes, it is determined that the radial and axial flows are not considered under stable conditions, and the continuity equation, radial and tangential momentum equations are obtained, which are expressed as:

[0056]

[0057] The boundary conditions are expressed as:

[0058]

[0059] The velocity distribution general solution expression v is obtained through the lubricating oil flow control equation group, which is expressed as:

[0060] Where r is the radius from any position in the wall oil film to the axis of rotation;

[0061] C oil,1 is a constant, C oil,2 is a constant, which is related to ω2, ω3, R2, and R3, where ω3 is the angular velocity of the high-pressure shaft and R3 is the inner diameter of the high-pressure shaft; and:

[0062]

[0063] In this step, it is necessary to first obtain the initial conditions for calculating the wall oil film velocity distribution relationship, including: high and low pressure rotor rotation angular velocity ω3, ω1, high and low pressure shaft radius R3, R1, oil film thickness range δ oil , where the wall oil film thickness δ oil Based on the numerical calculation of the oil collecting structure of the counter-rotating annular cavity; secondly, the boundary conditions for calculating the wall oil film velocity distribution are determined, including: the tangential velocity ω2R2 of the oil-gas interface, the wall velocity ω3R3 of the high-pressure rotor shaft, and finally the viscous shear force expression of the oil-gas interface is defined It is expressed as:

[0064]

[0065] Among them, δ oil is the thickness range of the lubricating oil film layer, and: oil =R3-R2, μ oil is the dynamic viscosity of lubricating oil.

[0066] The thickness range of the lubricating oil film layer is obtained by executing step S113 before obtaining the initial conditions for calculating the wall oil film velocity distribution relationship, which specifically includes:

[0067] After establishing the geometric model of the oil collecting structure of the counter-rotating annular cavity, the calculation area is discretized; the initial conditions and the physical parameters of the lubricating oil and air are determined simultaneously, and the solver parameters are set based on the VOF method and the sliding network technology to perform unsteady-state solution to obtain the volume fraction distribution of the lubricating oil and air at different angles along the circumferential section and the thickness distribution of the lubricating oil film layer; the tangential velocity distribution along the radial direction in the annular cavity is extracted to identify the mixed interface position of the lubricating oil film layer and the air layer; the thickness range of the lubricating oil film layer δ is obtained. oil .

[0068] Next, the velocity distribution model of the lubricating oil-air two-phase flow in the annular cavity is established, including the following steps:

[0069] Step S120: According to the relationship between the shear stress expression at the outer wall of the low-pressure shaft and the oil-gas interface and the viscous shear stress expression at the oil-gas interface, calculate the unknown quantities of the velocity distribution model of the lubricating oil-air two-phase flow in the counter-rotating annular cavity; the unknown quantities include: the shear stress at the outer wall of the low-pressure shaft Shear stress τ at the oil-gas interface oil,air (Viscous shear force at the oil-gas interface ), angular velocity of oil-gas interface ω2;

[0070] In this step, the shear stress at the outer wall of the low-pressure shaft is solved by combining formula (2), formula (3), and formula (10): Shear stress τ at the oil-gas interface oil,air(Viscous shear force at the oil-gas interface ), angular velocity of oil-gas interface ω2;

[0071] Step S130: determining boundary conditions for the velocity distribution model of the lubricating oil-air two-phase flow in the annular cavity;

[0072] This step can be based on the dimensionless height y of each layer in the Karman three-layer velocity distribution structure of the flat plate turbulent boundary layer. + The distribution of the viscous bottom layer (y + ≤5), buffer layer area (5<y + ≤30), turbulent core area (y + >30) thickness range, friction speed and the constants A, B, C, D, and E in the three-layer velocity distribution of Karman;

[0073] Among them, constants A, B, and D related to the rotating Reynolds number are defined, and linear regression is used to give the expressions of constants A, B, and D and the rotating Reynolds number, which are expressed as:

[0074]

[0075] C and E are constants, which are obtained by numerical calculation of the oil-air two-phase flow in the counter-rotating annular cavity, such as:

[0076] C1=C2=-3.05E1=2.34E2=5.84,

[0077] are the friction speeds, expressed as: y + is the dimensionless height, expressed as υ air is the kinematic viscosity of air.

[0078] Step S140: obtaining a tangential velocity distribution model in a counter-rotating annular cavity with a wall oil film, wherein the tangential velocity distribution model in the counter-rotating annular cavity is used to calculate the flow characteristics of the lubricating oil-air two-phase flow in the high-speed counter-rotating annular cavity;

[0079] In the present invention, the tangential velocity distribution model in the counter-rotating annular cavity with wall oil film includes the tangential velocity distribution in the radial direction of the low-pressure shaft outer wall, the tangential velocity distribution in the radial direction of the oil-gas interface, and the wall oil film velocity distribution.

[0080] The velocity distribution of the oil film on the wall is shown in formula (7). The tangential velocity distribution of the outer wall of the low-pressure shaft in the radial direction is expressed as:

[0081]

[0082] Secondly, the tangential velocity distribution in the radial direction of the oil-gas interface is expressed as:

[0083]

[0084] Formula (7), formula (11) and formula (12) together constitute the velocity distribution expression of the oil-air two-phase flow in the counter-rotating annular cavity, which can be used to calculate the flow characteristics of the oil-air two-phase flow in the high-speed counter-rotating annular cavity of an aircraft engine.

[0085] The present invention proposes a method for calculating the flow characteristics of two-phase flow in a counter-rotating annular cavity based on flow phenomena. By combining CFD numerical simulation, Karman three-layer structure velocity distribution and rotating flow test correlation, a lubricating oil and air flow model of a counter-rotating annular cavity with a lubricating oil film layer attached is established, and an analytical velocity distribution expression is defined, which provides a simple and effective method for calculating the flow characteristics of two-phase flow in a counter-rotating annular cavity.

[0086] The above disclosures are only several specific embodiments of the present invention; however, the present invention is not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for calculating the flow characteristics of lubricating oil-air two-phase flow in a high-speed counter-rotating annular cavity, characterized in that: The following steps are involved: Determine the assumptions of the interaxial flow model of the counter-rotating shaft cavity with the presence of wall oil film, wherein the assumptions are used for the oil-air two-phase flow under stable working conditions; Establish the air velocity distribution in the annular cavity and determine the shear stress expression at the outer wall of the low-pressure shaft and the oil-gas interface; Establish the wall oil film velocity distribution and determine the expression of viscous shear stress at the oil-gas interface; According to the shear stress expressions at the outer wall of the low-pressure shaft and the oil-gas interface and the viscous shear stress expression at the oil-gas interface, the unknown quantities of the velocity distribution model of the lubricating oil-air two-phase flow in the counter-rotating annular cavity are calculated; Determining boundary conditions for the velocity distribution model of the lubricating oil-air two-phase flow in the annular cavity; A tangential velocity distribution model in a counter-rotating annular cavity with a wall oil film is obtained, and the tangential velocity distribution model in the counter-rotating annular cavity is used to calculate the flow characteristics of the lubricating oil-air two-phase flow in a high-speed counter-rotating annular cavity.

2. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 1, characterized in that: The expressions for determining the shear stress at the outer wall of the low-pressure shaft and the oil-gas interface include: Based on the experimental correlation between the velocity distribution structure of the Karman three-layer of the flat plate turbulent boundary layer and the rotating shaft torque coefficient, the low-pressure rotor shaft torque coefficient C is determined. m1 ; Introducing the correction coefficient affected by Taylor vortex, the shear stress expression at the outer wall of the low-pressure axis is determined Based on the condition that the shear stress at the oil-gas interface and the outer wall of the low-pressure shaft produce the same torque, the shear stress expression τ at the oil-gas interface is determined. oil,air , expressed as: Among them, ω1 is the angular velocity of the low-pressure shaft, ω2 is the angular velocity of the oil-gas interface, and ρ air is the air density, C m1 is the torque coefficient of the low-pressure rotor shaft, R1 and R2 are the outer diameter of the low-pressure shaft and the radius of the oil-gas interface from the rotation axis, respectively, and Re1 is the Reynolds number of the low-pressure shaft rotation.

3. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 1, characterized in that: The expression for determining the viscous shear stress at the oil-gas interface includes: Establish the relationship between the velocity distribution of the oil film on the wall; Obtain the initial conditions for calculating the wall oil film velocity distribution relationship, including: high and low pressure rotor rotation angular velocity ω3, ω1, high and low pressure shaft radius R3, R1, oil film thickness range δ oil , where the wall oil film thickness δ oil Based on the numerical calculation of the oil collecting structure of the counter-rotating annular cavity; Determine the boundary conditions for calculating the wall oil film velocity distribution relationship, including: the tangential velocity of the oil-gas interface ω2R2, the high-pressure rotor shaft wall velocity ω3R3; Define the expression of viscous shear force at the oil-gas interface It is expressed as: Among them, δ oil is the thickness range of the lubricating oil film layer, and: oil =R3-R2,μ oil is the dynamic viscosity of lubricating oil.

4. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 3, characterized in that: Before obtaining the initial conditions for calculating the wall oil film velocity distribution relationship, the thickness range of the lubricating oil film layer δ is obtained by rotating the geometric model of the annular cavity oil collecting structure. oil ,include: Establish the geometric model of the counter-rotating annular cavity oil collecting structure; Perform regional discretization processing; Based on the VOF method and sliding network technology, the solver parameters are set to perform unsteady-state solutions; Obtain the distribution of lubricating oil and air volume fractions and the thickness of lubricating oil film at different circumferential cross sections; Extract the radial tangential velocity distribution in the annular cavity and identify the mixed interface position between the lubricating oil film layer and the air layer; Get the thickness range of the lubricating oil film layer δ oil .

5. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 3, characterized in that: When establishing the wall oil film velocity distribution relationship, based on the Couette flow between the two rotating shafts, it is determined that the radial and axial flows are not considered under stable conditions, and the continuity equation, radial and tangential momentum equations are obtained, which are expressed as:

6. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 1, characterized in that: The tangential velocity distribution model in the counter-rotating annular cavity with wall oil film includes the tangential velocity distribution in the radial direction of the outer wall of the low-pressure shaft, the tangential velocity distribution in the radial direction of the oil-gas interface, and the wall oil film velocity distribution.

7. The method for calculating the flow characteristics of the lubricating oil-air two-phase flow according to claim 6, characterized in that: The wall oil film velocity distribution is expressed as: Where r is the radius of any position in the wall oil film from the rotation axis, C oil,1 is a constant, C oil,2 is a constant, which is related to ω2, ω3, R2, and R3, where ω3 is the angular velocity of the high-pressure shaft, and R3 is the inner diameter of the high-pressure shaft, and: The tangential velocity distribution of the outer wall of the low-pressure shaft in the radial direction is expressed as: The tangential velocity distribution of the oil-gas interface in the radial direction is expressed as: Among them, A, B, and D are constants related to the rotating Reynolds number, and C and E are constants determined by numerical calculation of the oil-air two-phase flow in the counter-rotating annular cavity. are the friction speeds respectively.

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