Calculation method of gas-liquid two-phase nozzle configuration, program, equipment and storage medium

Abstract

The invention belongs to the technical field of underwater gas-liquid two-phase propulsion, and particularly relates to a gas-liquid two-phase nozzle configuration calculation method, program and equipment and a storage medium. On the basis of a split-phase flow model, a control equation set for describing the flow law of the gas-liquid two-phase spray pipe is established to replace a Rayleigh-Please equation, flow field parameters, including the average radius of bubbles, of the section of the spray pipe at a spray pipe inlet serve as initial conditions for solving, a target control equation set obtained after micro-differentiation is solved through a variable-step-size Runge-Kutta method, and the gas-liquid two-phase spray pipe flow law is obtained. Obtaining flow field parameters of the section of the nozzle at each flowing position in the gas-liquid two-phase nozzle, and further determining the configuration of the gas-liquid two-phase nozzle.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater gas-liquid two-phase propulsion, and specifically relates to a calculation method, program, device and storage medium for a gas-liquid two-phase nozzle configuration. Background Art

[0002] Underwater gas-liquid two-phase propulsion technology is an emerging propulsion method with advantages such as high propulsion efficiency and unlimited sailing speed. Introducing this technology into the field of water ramjet engines can significantly improve the propulsion efficiency of water ramjet engines and has extremely broad application prospects. Therefore, the design of gas-liquid two-phase nozzles is of great significance to the research of metal fuel gas-liquid two-phase water ramjet engines.

[0003] The gas-liquid two-phase flow motion model refers to the use of a set of equations to describe the changing laws of gas-liquid two-phase flow pressure, density and other parameters in the nozzle. Establishing a gas-liquid two-phase flow motion model is the premise and basis for the design of a gas-liquid two-phase nozzle.

[0004] Regarding the gas-liquid two-phase flow motion model, it currently mainly includes the homogeneous flow model and the phase separation flow model. Based on the phase separation flow, the drift flow model and the two-fluid model are derived. The homogeneous flow model is simple in form, involves fewer variables, and is relatively simple to solve, but does not consider the interaction between the phases. The theoretical calculation results are usually quite different from the experimental values. The phase separation flow model takes into account the interaction between the two phases, and the calculation results are more accurate than the homogeneous flow model.

[0005] To realize the design of gas-liquid two-phase nozzle, the most critical thing is to solve the group of motion equations. The group of motion equations in a large number of reference materials contains the Rayleigh-Plesset equation. The function of the Rayleigh-Plesse equation is to describe the change of bubble radius. Since the pressure inside the water ramjet engine is very high, the inclusion of this equation is not conducive to the solution of the equation group.

[0006] Therefore, it is urgent to use other equations to replace the Rayleigh-Plesse equations, improve the convergence performance of the equation group, solve the equation group smoothly under high pressure, and realize the design of the nozzle configuration of the metal fuel gas-liquid two-phase water ramjet engine. Summary of the invention

[0007] The purpose of the present invention is to provide a calculation method, program, device and storage medium for a gas-liquid two-phase nozzle configuration, which can solve the problem in the prior art that the Rayleigh-Plesse equation is difficult to solve under high pressure and the gas-liquid two-phase nozzle configuration design cannot be realized.

[0008] A method for calculating a gas-liquid two-phase nozzle configuration comprises the following steps:

[0009] Step 1: Based on the split-phase flow model, establish a set of control equations describing the flow law of the gas-liquid two-phase nozzle;

[0010] Step 2: Differentiate the control equations describing the flow law of the gas-liquid two-phase nozzle to generate the target control equations in differential form;

[0011] Step 3: Obtain the flow field parameters of the nozzle cross section at the nozzle inlet, and use the variable step-size Runge-Kutta method to solve the differential form of the target control equations to obtain the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle;

[0012] Step 4: Determine the configuration of the gas-liquid two-phase nozzle according to the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle.

[0013] Furthermore, in step 1, a group of control equations describing the flow law of the gas-liquid two-phase nozzle is established, specifically including: the continuity equation of the gas phase, the continuity equation of the liquid phase, the momentum conservation equation in the variable cross-section pipe flow, the bubble compressibility equation, the bubble mass conservation equation, the bubble energy conservation equation, the bubble momentum conservation equation and the liquid phase velocity distribution equation in the nozzle.

[0014] Furthermore, the continuity equation of the gas phase is:

[0015] ρ g αAV=const

[0016] Among them, ρ g represents the gas density on the current section of the nozzle; α represents the gas content on the current section of the nozzle; A represents the cross-sectional area of ​​the nozzle on the current section of the nozzle; V represents the average velocity of the gas phase on the current section of the nozzle; const represents a constant;

[0017] The continuity equation of the liquid phase is:

[0018] ρ l (1-α)AU=const

[0019] Among them, ρ l represents the density of the liquid; U represents the average velocity of the liquid phase on the current cross section of the nozzle;

[0020] The momentum conservation equation in the variable cross-section pipe flow is:

[0021]

[0022] Where p represents the pressure on the current section of the nozzle; x represents the coordinate along the axial direction of the nozzle;

[0023] The bubble compressibility equation is:

[0024] p=ρ gR g T g

[0025] Where: R g is the gas constant; T g Represents the gas temperature on the current cross section of the nozzle;

[0026] The bubble mass conservation equation is:

[0027]

[0028] Where r represents the average radius of the bubble on the current section of the nozzle;

[0029] The bubble energy conservation equation is:

[0030]

[0031] Among them, h c represents the convective heat transfer coefficient between bubbles and fluid; T l Represents the temperature of the liquid; C vg represents the specific heat capacity of the gas at constant volume; represents the species derivative based on the gas phase velocity;

[0032] The bubble momentum conservation equation is:

[0033]

[0034] Among them, C D represents the bubble resistance coefficient;

[0035] The liquid phase velocity distribution equation in the nozzle is:

[0036] U(x)=U0+300x 2

[0037] Among them, U0 represents the initial velocity of the liquid phase at the nozzle inlet, which is numerically equal to the initial average velocity at the nozzle inlet; x is the axial coordinate variable.

[0038] Furthermore, the continuity equation of the gas phase after differentiation is:

[0039]

[0040] The continuity equation of the liquid phase after differentiation is:

[0041]

[0042] The momentum conservation equation in the variable cross-section pipe flow after differentiation is:

[0043]

[0044] The bubble compressibility equation after differentiation is:

[0045]

[0046] The bubble mass conservation equation after differentiation is:

[0047]

[0048] The bubble energy conservation equation after differentiation is:

[0049]

[0050] The bubble momentum conservation equation after differentiation is:

[0051]

[0052] The differential equation for the liquid phase velocity distribution in the nozzle is:

[0053]

[0054] Furthermore, the flow field parameters of the nozzle section at the nozzle inlet in step 3 include the average bubble radius r0, gas content α0, average velocity V0 of the gas phase, cross-sectional area A0, pressure p0, gas temperature T g0 and gas density ρ g0 ;

[0055] Among them, the average bubble radius r0 of the nozzle cross section at the nozzle inlet is obtained using the prediction formula:

[0056]

[0057] Where We is the Weber number of the gas, d h represents the characteristic size of the reaction zone of the metal fuel; w g represents the burning rate of metal fuel; σ represents the surface tension coefficient; μ l Represents the dynamic viscosity of the liquid; Q represents the volume flow rate of the gas, Q = 4πr c 2 w g ; g represents the acceleration due to gravity; r c represents the particle size of metal fuel particles; p sat Represents the saturated vapor pressure.

[0058] Furthermore, the process of solving the problem using the variable step-size Runge-Kutta method in step 3 is specifically as follows:

[0059] Step 3.1: Initialize the current step number i=1, set the pressure threshold and the initial step length Δx, where x0 represents the nozzle inlet;

[0060] Substitute the flow field parameters of the nozzle cross section at the nozzle inlet into the differential form of the target control equation group to obtain the flow field parameters of the nozzle cross section at the flow position x1=x0+Δx;

[0061] Step 3.2: Set x i Substitute the flow field parameters of the nozzle section at the flow position into the differential form of the target control equations to obtain x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position;

[0062] Step 3.3: If Then reduce the step size, set Δx = Δx / 2, return to step 3.2, and recalculate x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position;

[0063] like Then increase the step size, set Δx = 1.1 × Δx, and execute step 3.4;

[0064] like Then the step length Δx remains unchanged and step 3.4 is executed;

[0065] Step 3.4: If the solved x i+1 Pressure p in the nozzle cross section at the flow location i+1 If it is greater than the set pressure threshold, set i=i+1 and return to step 3.2; otherwise, output the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle obtained in the iteration.

[0066] Furthermore, the value range of setting the initial step size is (0,10 -4 ); the pressure threshold is set to the external environmental pressure at the nozzle outlet obtained by measurement.

[0067] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned method for calculating the gas-liquid two-phase nozzle configuration.

[0068] A computer-readable storage medium stores a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the gas-liquid two-phase nozzle configuration.

[0069] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the gas-liquid two-phase nozzle configuration.

[0070] The beneficial effects of the present invention are:

[0071] Based on the phase flow model, the present invention establishes a control equation group describing the flow law of the gas-liquid two-phase nozzle to replace the Rayleigh-Plesse equation, takes the flow field parameters of the nozzle cross section at the nozzle inlet including the average radius of the bubble as the initial conditions for solution, uses the variable step-length Runge-Kutta method to solve the differentiated target control equation group, obtains the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle, and then determines the configuration of the gas-liquid two-phase nozzle. The present invention solves the problem in the prior art that the Rayleigh-Plesse equation is not conducive to solving the equation group due to the high pressure inside the water ramjet engine. The present invention can improve the convergence performance of the equation group, so that the target control equation group can be solved smoothly under high pressure, thereby obtaining the flow law of the flow field parameters in the gas-liquid two-phase nozzle, and based on the change law of the cross-sectional area of ​​the nozzle along the axial direction of the nozzle in the flow law of the flow field parameters in the gas-liquid two-phase nozzle, completes the design and calculation of the gas-liquid two-phase nozzle configuration. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 It is a schematic flow chart of a method for calculating a gas-liquid two-phase nozzle configuration in the present invention.

[0073] Figure 2 Schematic diagram of the change rule of the nozzle radius calculated in the embodiment of the present invention. DETAILED DESCRIPTION

[0074] The present invention is further described below in conjunction with the accompanying drawings.

[0075] The flow in the gas-liquid two-phase nozzle is essentially a "bubble flow". The gas in the gas-liquid two-phase flow exists in the form of bubbles, and the change law of the bubble size indirectly reflects the changes in other parameters along the nozzle (pressure, gas density, etc.). In order to describe the change law of bubble size, the Rayleigh-Plesset equation is currently generally used to describe the nonlinear relationship between bubble size and flow field pressure. However, under high-pressure conditions, the gas-liquid two-phase flow of the nozzle will have a transonic region, resulting in a sharp drop in pressure, causing the Rayleigh-Plesset equation to be difficult to solve, and is not suitable for metal fuel-gas-liquid two-phase water ramjet engines. The method used in the present invention can improve the convergence performance of the equation group, so that the equation group can be solved smoothly under high pressure, and the design of the gas-liquid two-phase nozzle of the water ramjet engine can be realized. Based on the split-phase flow model, the velocity difference between the gas and liquid phases and the change of the bubble radius with pressure are considered. The control equations in the traditional split-phase flow model are simplified, the convergence of the model solution is improved, and the flow law of the relevant parameters in the gas-liquid two-phase nozzle is calculated.

[0076] like Figure 1 As shown, the present invention provides a method for calculating a gas-liquid two-phase nozzle configuration, comprising:

[0077] Based on the split-phase flow model, a group of control equations describing the flow law of the gas-liquid two-phase nozzle is established, including: the continuity equation of the gas phase, the continuity equation of the liquid phase, the momentum conservation equation in the variable cross-section pipe flow, the state equation, the bubble mass conservation equation, the bubble energy conservation equation, and the bubble momentum conservation equation; among them, the state equation is used to describe the compressibility of the bubble. In the gas-liquid two-phase flow, the gas phase is assumed to be an ideal gas phase, and the parameters of the gas phase follow the state equation.

[0078] The continuity equation for the gas phase is:

[0079] ρ g αAV=const (1)

[0080] Among them, ρ g Represents the gas density on the current cross section of the nozzle, in kg / m 3 ; α represents the air content on the current section of the nozzle; A represents the cross-sectional area of ​​the nozzle on the current section of the nozzle, the unit is m 2 ; V represents the average velocity of the gas phase in the current cross section of the nozzle; const represents a constant.

[0081] The continuity equation for the liquid phase is:

[0082] ρ l (1-α)AU=const (2)

[0083] Among them, ρ l Represents the density of the liquid in kg / m 3 ; U represents the average velocity of the liquid phase in the current cross section of the nozzle, and the unit is m / s.

[0084] The momentum conservation equation in a variable cross-section pipe flow is:

[0085]

[0086] Among them, p represents the pressure on the current cross section of the nozzle, the unit is Pa; x represents the coordinate along the axial direction of the nozzle, the unit is m.

[0087] The bubble compressibility equation is:

[0088] p=ρ g R g T g (4)

[0089] Where: R g is the gas constant, the unit is J / kg·K -1 ; T gRepresents the gas temperature at the current cross section of the nozzle, in K.

[0090] The bubble mass conservation equation is:

[0091]

[0092] Where r represents the average radius of the bubble on the current cross section of the nozzle, in meters.

[0093] The bubble energy conservation equation is:

[0094]

[0095] Where: h c Represents the convection heat transfer coefficient between bubbles and fluid, the unit is W / m 2 ·K -1 ; T l Represents the temperature of the liquid in K; C vg Represents the specific heat capacity of the gas at constant volume, in J / kg·K -1 ; represents the material derivative based on the gas phase velocity. In a one-dimensional steady flow, Convective heat transfer coefficient h c Calculated by the following formula:

[0096]

[0097] Where: Nu is the Nusselt number; λ is the thermal conductivity, the unit is W / m·K -1 ;Re B is the bubble Reynolds number; μ g , μ l Represents the dynamic viscosity of gas and liquid respectively, the unit is Pa·s; Pr is the Prandtl number; C pl is the constant pressure specific heat capacity of the liquid, in J / kg·K -1 .

[0098] The bubble momentum conservation equation is:

[0099]

[0100] Among them, C D Represents the air bubble resistance coefficient.

[0101] Where: represents the material derivative with respect to the liquid phase. In a one-dimensional steady flow, C D Represents the bubble resistance coefficient, which is related to the bubble Reynolds number Re B The function is calculated by the following formula:

[0102]

[0103] Among them, other equations [Formula (4) and Formula (5))] are used to replace the Rayleigh-Plesse equation to improve the convergence performance of the equation group, so that the equation group can be solved smoothly under high pressure, and the design of the gas-liquid two-phase nozzle of the water ramjet engine is realized.

[0104] In practical applications, when the cross-street area A of the nozzle is an unknown quantity, the above target control equations will not be closed, so a method for the distribution of the liquid phase velocity U(x) in the nozzle is added.

[0105] The control equations also include the calculation formula for the distribution of the liquid phase velocity U(x) in the nozzle:

[0106] U(x)=U0+300x 2 (13)

[0107] Among them, U0 represents the initial velocity of the liquid phase at the nozzle inlet, and the initial velocity is equal to the initial average velocity at the nozzle inlet.

[0108] Among them, formula (1) to formula (6) and formula (11) constitute the basic motion equations describing the gas-liquid two-phase flow, namely the control equations. Among them, the flow field parameters that need to be solved are: gas content α, gas flow rate V, cross-sectional area A, pressure p, gas temperature T g , gas density ρ g , bubble radius r, there are 7 flow field parameters to be solved, and the calculation model contains 7 independent description equations. Therefore, the control equation group is closed and can be solved. There are seven flow field parameters to be solved, and there are seven linearly independent equations listed. The equation group is closed, and the change law of the flow field parameters can be solved.

[0109] Differentiate the split-phase flow control equations, using x as the axial coordinate variable. The differentiation process of the equations is the differentiation of all variables in the equations with respect to the axial coordinate x to form a closed first-order differential equation group. The specific process is as follows:

[0110] The continuity equation of the gas phase after differentiation is:

[0111]

[0112] The continuity equation of the liquid phase after differentiation is:

[0113]

[0114] The momentum conservation equation in the variable cross-section pipe flow after differentiation is:

[0115]

[0116] The bubble compressibility equation after differentiation is:

[0117]

[0118] The bubble mass conservation equation after differentiation is:

[0119]

[0120] The bubble energy conservation equation after differentiation is:

[0121]

[0122] The bubble momentum conservation equation after differentiation is:

[0123]

[0124] By adjusting the above differentiated target control equations, we can get the form of A·x=B, where A is a matrix of 7 rows and 7 columns, and x and B are 7th-order column vectors.

[0125] Taking formula (15) as an example, it can be sorted into the following form:

[0126]

[0127] The remaining differentiated equations are arranged in the same way and will not be repeated here.

[0128] The flow field parameters of the nozzle cross section at the nozzle inlet are obtained as initial parameters, and the average bubble radius r0 of the nozzle cross section at the nozzle inlet is predicted based on the preset formula:

[0129]

[0130] in:

[0131]

[0132] Q=4πr c 2 w g (27)

[0133] Where We is the Weber number of the gas; d h represents the characteristic size of the reaction zone of the metal fuel; w g represents the burning rate of metal fuel; σ represents the surface tension coefficient; μ l represents the dynamic viscosity of the liquid; Q represents the volume flow rate of the gas; g represents the acceleration due to gravity; r c represents the particle size of metal fuel particles; p sat Represents the saturated vapor pressure.

[0134] In practical applications, the accuracy of the initial radius prediction directly determines whether the differential form of the target control equations can be successfully solved and the accuracy of the solution.

[0135] According to the Runge-Kutta method with initial parameters and variable step size, the target control equation group is solved to obtain the flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle; the flow field parameters to be solved include the gas content on the current section of the nozzle, the average velocity on the current section of the nozzle, the cross-sectional area on the current section of the nozzle, the pressure on the current section of the nozzle, the gas temperature on the current section of the nozzle, the gas density on the current section of the nozzle and the average radius of the bubble on the current section of the nozzle; the flow law is the flow trend of the flow field parameters of each section of the solved nozzle configuration.

[0136] According to the initial parameters and the Runge-Kutta method with variable step length, the target control equation group is solved to obtain the flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle, which specifically includes:

[0137] In the whole solution process of the variable step-size Runge-Kutta method, the initial step-sizes of two adjacent steps are the same; the step-size is the distance between the flow positions of two adjacent steps;

[0138] Substitute the initial parameters into the target control equation group to obtain the flow field parameters on the nozzle cross section solved at the current step flow position, and obtain the pressure on the nozzle cross section solved at the current step flow position;

[0139] According to the initial step length and the flow field parameters on the nozzle cross section solved at the current step flow position, the pressure on the nozzle cross section corresponding to the second step flow position is determined;

[0140] According to the pressure on the nozzle cross section solved at the current step flow position and the pressure on the nozzle cross section corresponding to the second step flow position, the relative change value of the pressure of adjacent steps is determined;

[0141] Determine the target flow position of the second step based on the relative change value of the pressure between adjacent steps;

[0142] The flow field parameters solved at the target flow position in the second step are used as the flow field parameters on the nozzle cross section corresponding to the flow position in the second step;

[0143] Based on the flow field parameters on the nozzle cross section corresponding to the second-step flow position and the initial step length, the flow field parameters on the nozzle cross section corresponding to the third-step flow position are determined, and the third-step flow position is used as the current-step flow position to determine the flow field parameters of the nozzle cross section corresponding to each flow position of the nozzle configuration in turn; the flow trend of the flow field parameters of each nozzle cross section of the nozzle configuration is used as the flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle.

[0144] In practical applications, in order to ensure that a stable numerical solution can be obtained when the pressure changes over a large range, that is, to obtain the flow law of relevant parameters in the gas-liquid two-phase nozzle, the Runge-Kutta method with a variable step size is used.

[0145] The specific process of solving the problem using the variable step-size Runge-Kutta method is as follows:

[0146] Step 1: Initialize the current step number i=1, set the pressure threshold and the initial step length Δx, where x0 represents the nozzle inlet;

[0147] In order to prevent the solved flow field parameters from diverging or reporting errors, the flow field parameters may change drastically at certain positions along the nozzle axis. If the step size is too large, it will cause calculation errors and the flow law cannot be calculated. Therefore, the initial step size should not be too large, and should be (0,10 -4 ); the pressure threshold can be set to the external environmental pressure at the nozzle outlet obtained by measurement, that is, it is determined that the gas-liquid two-phase nozzle itself has been solved by iteration here;

[0148] Substitute the flow field parameters of the nozzle cross section at the nozzle inlet into the differential form of the target control equation group to obtain the flow field parameters of the nozzle cross section at the flow position x1=x0+Δx;

[0149] x i The flow field parameters of the nozzle section at the flow position include: the average bubble radius r of the nozzle section i , gas content α i , the average velocity of the gas phase V i , cross-sectional area A i , pressure p i , gas temperature T gi and gas density ρ gi ;

[0150] Step 2: Set x i Substitute the flow field parameters of the nozzle section at the flow position into the differential form of the target control equations to obtain x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position;

[0151] Step 3: If Then reduce the step size, set Δx = Δx / 2, return to step 2, and recalculate x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position;

[0152] like Then increase the step size, set Δx = 1.1 × Δx, and execute step 4;

[0153] like Then the step length Δx remains unchanged and step 4 is executed;

[0154] Step 4: If the solved x i+1 Pressure p in the nozzle cross section at the flow location i+1 If it is greater than the set pressure threshold, set i=i+1 and return to step 2; otherwise, output the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle obtained in the iteration.

[0155] Finally, the configuration of the gas-liquid two-phase nozzle is determined according to the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle.

[0156] Embodiment 1:

[0157] Referring to Table 1, the parameter values ​​required for calculating the initial radius of the bubble are set to predict the initial radius of the bubble.

[0158] Table 1 Parameters required to predict the initial radius of bubbles

[0159] <![CDATA[d h (one)]]> <![CDATA[ρ g (kg / m 3 )]]> <![CDATA[ρ l (kg / m 3 )]]> <![CDATA[w g (m / s)]]> σ(N / m) 44 8.00 998.0 0.2 0.072 <![CDATA[μ l (Pa·s)]]> <![CDATA[r c (one)]]> <![CDATA[p sat (kPa)]]> <![CDATA[p0(kPa)]]> —— 0.001 44.0 935.31 1200.0 ——

[0160] Substituting the parameters in Table 1 into formulas (22)-(27), the Weber number of the gas under this condition is calculated to be We = 0.0031, and the predicted value of the initial radius of the bubble is r0 = 0.762 mm.

[0161] Referring to Table 2, the initial parameters in Table 2 are used as the initial conditions for solving the target control equations. The target control equations after differentiation are solved, and the initial step size is 10 -5 , the variable step-size Runge-Kutta method is used to solve the differentiated target control equations, and the flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle is obtained.

[0162] Table 2 Initial parameters of the gas-liquid two-phase nozzle inlet

[0163] <![CDATA[α0]]> <![CDATA[V0(m / s)]]> <![CDATA[A0(m 2 )]]> <![CDATA[p0(kPa)]]> <![CDATA[T g0 (K)]]> <![CDATA[ρ g0 (kg / m 3 )]]> <![CDATA[r0(mm)]]> 0.7 0.8435 <![CDATA[7.85×10 -3 ]]> 1200.0 350.0 8.00 0.762

[0164] The inlet parameters in Table 2 are used as initial conditions to solve the differential equation and the nozzle outlet pressure p is taken as e =199125Pa as the pressure threshold, when the solution pressure p drops to the outlet pressure p e Terminate the calculation.

[0165] The flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle is calculated, including: gas content α, gas flow rate V, cross-sectional area A, pressure p, gas temperature T g , gas density ρ g , bubble radius r. Figure 2 , R represents the nozzle radius, D represents the axial length, according to the change law of the nozzle radius R, using Design the nozzle configuration.

[0166] Based on the split-phase flow model, the present invention establishes a group of control equations describing the flow law of the gas-liquid two-phase nozzle, predicts the initial radius of the bubble, and uses the variable-step Runge-Kutta method to calculate the flow law of the flow field parameters to be solved in the gas-liquid two-phase nozzle, which can provide a reference for the design of the nozzle configuration of the metal fuel-gas-liquid two-phase water ramjet engine.

[0167] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the configuration of a gas-liquid two-phase nozzle, characterized in that: The following steps are involved: Step 1: Based on the split-phase flow model, establish a control equation group describing the flow law of the gas-liquid two-phase nozzle; Step 2: Differentiate the control equations describing the flow law of the gas-liquid two-phase nozzle to generate the target control equations in differential form; Step 3: Obtain the flow field parameters of the nozzle cross section at the nozzle inlet, and use the variable step-size Runge-Kutta method to solve the differential form of the target control equations to obtain the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle; Step 4: Determine the configuration of the gas-liquid two-phase nozzle according to the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle.

2. The method for calculating the gas-liquid two-phase nozzle configuration according to claim 1, characterized in that: In the step 1, a group of control equations describing the flow law of the gas-liquid two-phase nozzle is established, specifically including: the continuity equation of the gas phase, the continuity equation of the liquid phase, the momentum conservation equation in the variable cross-section pipe flow, the bubble compressibility equation, the bubble mass conservation equation, the bubble energy conservation equation, the bubble momentum conservation equation and the liquid phase velocity distribution equation in the nozzle.

3. The method for calculating the gas-liquid two-phase nozzle configuration according to claim 2, characterized in that: The continuity equation of the gas phase is: r g αAV=const Among them, ρ g represents the gas density on the current section of the nozzle; α represents the gas content on the current section of the nozzle; A represents the cross-sectional area of ​​the nozzle on the current section of the nozzle; V represents the average velocity of the gas phase on the current section of the nozzle; const represents a constant; The continuity equation of the liquid phase is: r l (1-a)AU=const Among them, ρ l Represents the density of the liquid; U represents the average velocity of the liquid phase on the current cross section of the nozzle; The momentum conservation equation in the variable cross-section pipe flow is: Where p represents the pressure on the current section of the nozzle; x represents the coordinate along the axial direction of the nozzle; The bubble compressibility equation is: p=ρ g R g T g Where: R g is the gas constant; T g Represents the gas temperature on the current cross section of the nozzle; The bubble mass conservation equation is: Where r represents the average radius of the bubble on the current section of the nozzle; The bubble energy conservation equation is: Among them, h c represents the convective heat transfer coefficient between bubbles and fluid; T l Represents the temperature of the liquid; C vg represents the specific heat capacity of the gas at constant volume; represents the species derivative based on the gas phase velocity; The bubble momentum conservation equation is: Among them, C D represents the bubble resistance coefficient; The liquid phase velocity distribution equation in the nozzle is: U(x)=U0+300x 2 Among them, U0 represents the initial velocity of the liquid phase at the nozzle inlet, which is numerically equal to the initial average velocity at the nozzle inlet; x is the axial coordinate variable.

4. The method for calculating the gas-liquid two-phase nozzle configuration according to claim 3, characterized in that: The step 2 is specifically as follows: The continuity equation of the gas phase after differentiation is: The continuity equation of the liquid phase after differentiation is: The momentum conservation equation in the variable cross-section pipe flow after differentiation is: The bubble compressibility equation after differentiation is: The bubble mass conservation equation after differentiation is: The bubble energy conservation equation after differentiation is: The bubble momentum conservation equation after differentiation is: The differential equation for the liquid phase velocity distribution in the nozzle is:

5. The method for calculating the gas-liquid two-phase nozzle configuration according to claim 4, characterized in that: The flow field parameters of the nozzle section at the nozzle inlet in step 3 include the average bubble radius r0, gas content α0, average velocity V0 of the gas phase, cross-sectional area A0, pressure p0, gas temperature T g0 and gas density ρ g0 ; Among them, the average bubble radius r0 of the nozzle cross section at the nozzle inlet is obtained using the prediction formula: Where We is the Weber number of the gas, d h represents the characteristic size of the reaction zone of the metal fuel; w g represents the burning rate of metal fuel; σ represents the surface tension coefficient; μ l Represents the dynamic viscosity of the liquid; Q represents the volume flow rate of the gas, Q = 4πr c 2 w g ; g represents the acceleration due to gravity; r c represents the particle size of metal fuel particles; p sat Represents the saturated vapor pressure.

6. A method for calculating a gas-liquid two-phase nozzle configuration according to claim 5, characterized in that: The specific process of solving the problem using the variable step-size Runge-Kutta method in step 3 is as follows: Step 3.1: Initialize the current step number i=1, set the pressure threshold and the initial step length Δx, where x0 represents the nozzle inlet; Substitute the flow field parameters of the nozzle cross section at the nozzle inlet into the differential form of the target control equation group to obtain the flow field parameters of the nozzle cross section at the flow position x1=x0+Δx; Step 3.2: Set x i Substitute the flow field parameters of the nozzle section at the flow position into the differential form of the target control equations to obtain x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position; Step 3.3: If Then reduce the step size, set Δx = Δx / 2, return to step 3.2, and recalculate x i+1 =x i Flow field parameters of the nozzle cross section at the +Δx flow position; like Then increase the step size, set Δx = 1.1 × Δx, and execute step 3.4; like Then the step length Δx remains unchanged and step 3.4 is executed; Step 3.4: If the solved x i+1 Pressure p in the nozzle cross section at the flow location i+1 If it is greater than the set pressure threshold, set i=i+1 and return to step 3.2; Otherwise, the flow field parameters of the nozzle cross section at each flow position in the gas-liquid two-phase nozzle obtained in the iteration are output.

7. The method for calculating the gas-liquid two-phase nozzle configuration according to claim 6, characterized in that: The value range of setting the initial step size is (0,10 -4 ); the pressure threshold is set to the external environmental pressure at the nozzle outlet obtained by measurement.

8. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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