Method and device for determining flow instability in a non-uniform heating channel

Abstract

The present invention provides a method and device for determining flow instability in a non-uniform heating channel. Based on a one-dimensional uniform flow model, the method comprises: Fourier expansion of non-uniform power distribution based on triangular basis functions; and determining flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution. The present invention can analyze flow instability in any non-uniform heating channel by Fourier expansion of any heat source based on triangular basis functions and based on a series of mathematical derivations, thereby broadening the application of uniform flow models in analyzing flow instability in non-uniform heating channels.

Description

Technical Field

[0001] The invention relates to the technical field of thermal hydraulic numerical simulation, and in particular to a method and a device for determining flow instability in a non-uniform heating channel. Background Art

[0002] Working fluid flow instability is a common phenomenon in thermal systems, which greatly affects the safety and stability of equipment and system operation.

[0003] Currently, most of the calculation methods for flow instability are constructed for uniform heating channels, but non-uniform heating occurs during the actual operation of the system. For example, the flow heat exchange of the coolant in the core of a nuclear reactor is caused by the physical design of the core and the rod insertion and withdrawal operations during transient operation, resulting in a non-uniform distribution of the core power along the coolant channel.

[0004] Therefore, proposing a method for determining flow instability in non-uniform heating channels is a technical problem that needs to be solved urgently. Summary of the invention

[0005] The present invention provides a method and device for determining flow instability in a non-uniform heating channel, so as to solve the defect that the flow instability determination method in the prior art is aimed at a uniform heating channel, while the system is actually a non-uniform heating channel.

[0006] The present invention provides a method for determining flow instability in a non-uniform heating channel, based on a one-dimensional uniform flow model, comprising:

[0007] The non-uniform power distribution is based on the Fourier expansion of triangular basis functions;

[0008] Flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion.

[0009] Optionally, the flow instability in the non-uniform heating channel is characterized by one or more of the following:

[0010] rate of change of boiling boundary;

[0011] rate of change of exit velocity;

[0012] The rate of change of outlet density.

[0013] Optionally, in a case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the boiling boundary, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0014] Determining the heat release of the non-uniform heating channel section based on the non-uniform power distribution after expansion;

[0015] The rate of change of the boiling boundary is determined based on the heat release of the non-uniform heating channel section and the enthalpy value in the single-phase region control body.

[0016] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0017] The rate of change of the outlet velocity is determined based on the expanded non-uniform power distribution, the working fluid density in the two-phase region in the non-uniform heating channel, and the inlet velocity.

[0018] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0019] Determine the voltage drop of each channel based on the expanded non-uniform power distribution;

[0020] The change rate of the outlet velocity of each channel is determined based on the pressure drop of each channel and the total channel flow.

[0021] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet density, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0022] determining a rate of change of a saturated liquid channel length based on the expanded non-uniform power distribution;

[0023] The change rate of the outlet density is determined based on the change rate of the saturated liquid channel length, the mass of the working fluid in the single-phase region in the non-uniform heating channel, and the mass of the working fluid in the two-phase region in the non-uniform heating channel.

[0024] Optionally, the enthalpy value in the single-phase region control volume is determined under the condition that the enthalpy value in the single-phase region is linearly distributed.

[0025] The present invention also provides a device for determining flow instability in a non-uniform heating channel, based on a one-dimensional uniform flow model, comprising:

[0026] An expansion module, used for Fourier expansion of non-uniform power distribution based on triangular basis functions;

[0027] A determination module is used to determine flow instability in the non-uniform heating channel based on the non-uniform power distribution after expansion.

[0028] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of any of the above-described methods for determining flow instability in a non-uniform heating channel are implemented.

[0029] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the above-described methods for determining flow instability in a non-uniform heating channel.

[0030] The present invention also provides a computer program product, comprising a computer program, which, when executed by a processor, implements the steps of any of the above-mentioned methods for determining flow instability in a non-uniform heating channel.

[0031] The method and device for determining flow instability in a non-uniform heating channel provided by the present invention can analyze the flow instability in any non-uniform heating channel by Fourier expansion of any heat source based on triangular basis functions and based on a series of mathematical derivations, thereby broadening the application of uniform flow models in the analysis of flow instability in non-uniform heating channels. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 is a flow chart of a method for determining flow instability in a non-uniform heating channel provided by an embodiment of the present invention;

[0034] Figure 2 is a schematic diagram of a non-uniform heating channel provided by an embodiment of the present invention;

[0035] Figure 3 is a schematic structural diagram of a device for determining flow instability in a non-uniform heating channel provided by an embodiment of the present invention;

[0036] Figure 4 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] Figure 1 FIG. 1 is a flow chart of a method for determining flow instability in a non-uniform heating channel provided by an embodiment of the present invention. Figure 1 As shown, the present invention provides a method for determining flow instability in a non-uniform heating channel, based on a one-dimensional uniform flow model, the method comprising:

[0039] Step 101: Fourier expansion of the non-uniform power distribution based on a triangular basis function.

[0040] Specifically, based on the one-dimensional uniform flow model, the following assumptions are made:

[0041] The vapor and liquid phases are in a state of thermodynamic equilibrium; the physical properties of the single-phase fluid in the channel are constants, which are the corresponding parameters under saturation pressure; the friction pressure drop in the two-phase region is calculated using a uniform flow model, ignoring viscosity dissipation; the coolant in the channel flows in one dimension.

[0042] For the convenience of analysis, the core power distribution under the steady-state condition of a uniform bare reactor is taken as an example for explanation. The power distribution of any other heat source may also be used for explanation, and the present invention is not limited to this.

[0043] Figure 2 Schematic diagram of a non-uniform heating channel provided by an embodiment of the present invention. Figure 2 As shown, the coordinate system is constructed with the center of the non-uniform heating channel as the origin. The vertical axis Z represents the height of the channel. The height of the entire non-uniform heating channel is L0, and the height of the single-phase zone is L0 / 2+L f , the height of the two-phase region is L0 / 2-L f , L f is the height of the boiling boundary, L0 / 2 is the channel exit, and -L0 / 2 is the channel entrance.

[0044] For a uniform bare pile steady state, the power distribution of its heat source can be expanded according to the triangular basis function. The expansion of the power distribution according to the triangular basis function is equivalent to the expansion of the heat release rate per unit area according to the triangular basis function. The expression of the heat release rate per unit area after expansion according to the triangular basis function is as follows:

[0045] q(z)=q0cos(zπ / L0)

[0046] Where q(z) is the heat release rate per unit area along the channel axis Z, q0 is the reference value of the heat release rate per unit area, z is the axial height, and L0 is the height of the entire non-uniform heating channel.

[0047] Step 102: determining flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution.

[0048] Specifically, the expanded non-uniform power distribution, that is, the heat release rate per unit area expanded according to the triangular basis function, is subjected to a series of mathematical derivations to determine the flow instability in the non-uniform heating channel.

[0049] Optionally, the flow instability in the non-uniform heating channel is characterized by one or more of the following:

[0050] rate of change of boiling boundary;

[0051] rate of change of exit velocity;

[0052] The rate of change of outlet density.

[0053] Specifically, the flow instability in the non-uniform heating channel can be characterized by one or more of the rate of change of the boiling boundary, the rate of change of the outlet velocity, or the rate of change of the outlet density, wherein the boiling boundary is the boundary between the single-phase region and the two-phase region.

[0054] For example, if the rate of change of the boiling boundary becomes larger, such as showing periodic fluctuations, and the numerical fluctuations diverge, it indicates that flow instability has occurred in the non-uniform heating channel.

[0055] For example, if the rate of change of the outlet velocity becomes larger, it indicates that flow instability has occurred in the non-uniform heating channel.

[0056] For example, if the rate of change of the outlet density becomes larger, it indicates that flow instability has occurred in the non-uniform heating channel.

[0057] Characterizing the flow instability in the non-uniform heating channel by the rate of change of the boiling boundary, the rate of change of the outlet velocity or the rate of change of the outlet density is helpful to further determine the flow instability in the non-uniform heating channel.

[0058] Optionally, in the case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the boiling boundary, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0059] Determine the heat release of the non-uniform heating channel section based on the non-uniform power distribution after expansion;

[0060] The rate of change of the boiling boundary is determined based on the heat release of the non-uniformly heated channel section and the enthalpy value in the single-phase region control body.

[0061] Specifically, the total heat release from the inlet to the height L along the axial direction can be determined according to the heat release rate per unit area. The expression of the total heat release from the inlet to the height L along the axial direction is as follows:

[0062]

[0063] In the formula, q tot (L) is the total heat release from the inlet -L0 / 2 to the height L, U h is the cross-sectional circumference of the non-uniform heating channel, q0 is the reference value of the heat release rate per unit area, z is the axial height of the channel, and L0 is the height of the entire non-uniform heating channel.

[0064] According to the total heat release from the inlet to the height L along the axial direction, the heat released from the height L n-1 To height L n The heat release of the interval section, from the height L n-1 To height L n The expression of heat release in the interval is as follows:

[0065]

[0066] Where q0 is the reference value of heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, L n-1 is the height of the n-1th section of the channel interval, L n is the height of the nth segment of the channel interval, and the subscript n is the number of segments in the channel interval.

[0067] Divide the single-phase area into multiple control bodies, that is, divide the channel from -L0 / 2 to L0 / 2+L f The control body is divided at the points, and the total number of control bodies is recorded as Nsp. The control body is equivalent to the interval segment of the single-phase channel.

[0068] Optionally, the enthalpy value in the single-phase region control volume is determined under the condition that the enthalpy value in the single-phase region is linearly distributed.

[0069] Specifically, when the enthalpy value in the single-phase region is distributed linearly, the enthalpy value in any control volume in the single-phase region can be linearly represented by the inlet enthalpy value and the saturation enthalpy value.

[0070] The expression of the enthalpy value of the nth control volume in the single-phase region is as follows:

[0071]

[0072] In the formula, h nis the enthalpy value of the nth control volume in the single-phase region, h in is the inlet enthalpy, Nsp is the total number of control bodies in the single-phase region, h f is the saturation enthalpy.

[0073] By determining the enthalpy value of the single-phase region under the condition that the enthalpy value of the single-phase region is linearly distributed, the calculation process of the enthalpy value of the single-phase region is simplified, which is conducive to further determining the flow instability in the non-uniform heating channel.

[0074] The expression of the uniform flow capacity conservation equation is as follows:

[0075]

[0076] In the formula, ρ is the density of the working fluid, h is the enthalpy value, u is the flow rate of the working fluid, q is the heat release, and U h is the cross-sectional circumference of the non-uniform heating channel, A is the cross-sectional area of ​​the non-uniform heating channel, t is the instantaneous time, and z is the axial height of the channel.

[0077] The Leibniz formula is expressed as follows:

[0078]

[0079] Substitute the calculation formula of the single-phase region enthalpy value into the uniform flow energy conservation equation, and convert the resulting equation from the height L n-1 To height L n Integrate and combine with the height L n-1 To height L n The heat release of the interval segment and the Leibniz formula can be used to obtain the expression of Formula 1 as follows:

[0080]

[0081] Where, L n is the height of the nth section of the channel interval, L n-1 is the height of the n-1th segment of the channel interval, u in is the inlet working fluid flow rate, q0 is the reference value of heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, A is the cross-sectional area of ​​the non-uniform heating channel, ρ is the working fluid density, h n is the enthalpy value of the single-phase region control body n, h n-1 is the enthalpy value of the single-phase region control body n-1, Nsp is the total number of single-phase region control bodies, h f is the saturation enthalpy, h in is the inlet enthalpy, and t is the instantaneous time.

[0082] Let n be Nsp, and by recursion we can get the boiling boundary L NspThe rate of change.

[0083] The heat release rate per unit area is first used to calculate the heat release of the non-uniform heating channel section, and then the heat release of the non-uniform heating channel section and the enthalpy value in the single-phase control body are used to calculate the change rate of the boiling boundary. Finally, the determined change rate of the boiling boundary is used to characterize the flow instability in the non-uniform heating channel, which provides a feasible solution for evaluating the flow instability in the non-uniform heating channel in actual operating conditions.

[0084] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0085] The rate of change of the outlet velocity is determined based on the expanded non-uniform power distribution, the working fluid density in the two-phase region in the non-uniform heating channel, and the inlet velocity.

[0086] Specifically, the expression of the continuity equation is as follows:

[0087]

[0088] Where ρ is the working fluid density, t is the instantaneous time, z is the axial height of the channel, and u is the working fluid flow rate.

[0089] Expanding the uniform flow energy conservation equation and eliminating related terms using the continuity equation, we can get the expression of formula 2 as follows:

[0090]

[0091] In the formula, ρ is the working fluid density, h is the enthalpy value, t is the instantaneous time, u is the working fluid flow rate, z is the axial height of the channel, q0 is the reference value of the heat release rate per unit area, and U is h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, and A is the cross-sectional area of ​​the non-uniform heating channel.

[0092] The expression of working fluid density is as follows:

[0093]

[0094] Where ρ is the density of the working fluid, ρ f is the density of the saturated liquid, v f is the specific volume of the saturated liquid, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated vapor, h is the enthalpy, h f is the saturation enthalpy.

[0095] From the expression of working fluid density, it can be seen that when the enthalpy value is less than or equal to the saturation enthalpy value, the corresponding working fluid density is the working fluid density in the single-phase region. The working fluid density in the single-phase region changes very little and can be approximately regarded as the density of the saturated liquid ρ f When the enthalpy value is greater than the saturation enthalpy value, the corresponding working fluid density is the working fluid density in the two-phase region, and the working fluid density in the two-phase region is related to the specific volume of the saturated liquid and the specific volume of the saturated vapor.

[0096] Substituting the working fluid density in the two-phase region into the continuity equation, the expression of Formula 3 can be obtained as follows:

[0097]

[0098] In the formula, v f is the specific volume of the saturated liquid, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated vapor, h is the enthalpy, h f is the saturation enthalpy value, u is the working fluid flow rate, z is the axial height of the channel, and t is the instantaneous time.

[0099] Combining Formula 2 and Formula 3, we can get the expression of Formula 4 as follows:

[0100]

[0101] In the formula, u is the working fluid flow rate, z is the axial height of the channel, q0 is the reference value of the heat release rate per unit area, and U h is the cross-sectional perimeter of the non-uniform heating channel, A is the cross-sectional area of ​​the non-uniform heating channel, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated steam, and L0 is the height of the entire non-uniform heating channel.

[0102] Formula 4 is converted into boiling boundary L f Integrate to the channel exit L0 / 2, and the expression of the channel exit velocity is as follows:

[0103]

[0104] In the formula, u out is the exit speed, u in is the inlet velocity (generally given as a boundary condition), q0 is the reference value of the heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, A is the cross-sectional area of ​​the non-uniform heating channel, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fgis the difference between the enthalpy of saturated liquid and the enthalpy of saturated steam, L0 is the height of the entire non-uniform heating channel, L f is the height of the boiling boundary.

[0105] will u out The rate of change of the outlet velocity can be obtained by taking the derivative of the outlet velocity with respect to time.

[0106] The rate of change of the outlet velocity is determined by calculating the heat release rate per unit area, the working fluid density in the two-phase region in the non-uniform heating channel, and the inlet velocity. The determined rate of change of the outlet velocity is then used to characterize the flow instability in the non-uniform heating channel, which provides a feasible solution for evaluating the flow instability in the non-uniform heating channel under actual operating conditions.

[0107] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0108] Determine the voltage drop of each channel based on the expanded non-uniform power distribution;

[0109] The change rate of the outlet velocity of each channel is determined based on the pressure drop of each channel and the total channel flow.

[0110] Specifically, for a reactor core with multiple parallel channels, the exit velocity of each channel needs to be determined.

[0111] The uniform flow momentum equation is expressed as follows:

[0112]

[0113] In the formula, ρ is the working fluid density, u is the working fluid flow rate, P is the pressure, z is the channel axial height, t is the instantaneous time, g is the gravity, f is the friction coefficient, and D e is the diameter of the channel cross section, k inlet is the form resistance coefficient at the channel entrance, k outlet is the shape resistance coefficient of the channel outlet, and Δz is the channel height difference.

[0114] By integrating the uniform flow equation along the channel, the expression for the total pressure drop in each channel can be obtained as follows:

[0115] ΔP tot =ΔP g +ΔP a +ΔP I +ΔP f

[0116] Where ΔP tot is the total pressure drop of each channel, ΔP gTo increase the pressure drop, ΔP a is the accelerating pressure drop, ΔP I is the inertial pressure drop, ΔP f is the friction pressure drop.

[0117] The heat released by the fuel pellets is determined by the core power. The heat released by the pellets is transferred to the coolant working fluid in the channel through cladding heat conduction and convection heat transfer, which in turn affects the density and related physical parameters of the working fluid. Therefore, the pressure drop of the coolant channel is affected by the non-uniform power distribution.

[0118] Increase pressure drop ΔP g The expression is as follows:

[0119]

[0120] Where ΔP g To increase the pressure drop, M ch is the total mass of the coolant in the channel, A is the cross-sectional area of ​​the non-uniform heating channel, and g is the gravity.

[0121] Acceleration pressure drop ΔP a The expression is as follows:

[0122]

[0123] Where ΔP a is the acceleration pressure drop, ρ is the working fluid density, u is the working fluid flow rate, z is the channel axial height, u in is the inlet velocity, u out is the outlet velocity, ρ out is the outlet density, ρ f is the density of the saturated liquid.

[0124] For the inertial pressure drop, it is necessary to integrate the single-phase region and the two-phase region respectively, and then introduce the channel equivalent density M ch / (AL0), the equivalent density of the two-phase region is M ch_TP / (A(L0 / 2-L f )), where M ch is the total mass of the coolant in the channel, AL0 is the channel volume, M ch_TP is the mass of the coolant in the two-phase region, A(L0 / 2-L f ) is the volume of the two-phase region, and combined with the channel outlet velocity u out The expression of inertial pressure drop ΔP is obtained I The expression is as follows:

[0125]

[0126] Where ρ is the working fluid density, u is the working fluid flow rate, t is the instantaneous time, z is the axial height of the channel, Mch is the total mass of the coolant in the channel, M ch_TP is the mass of the coolant in the two-phase region, A is the cross-sectional area of ​​the non-uniform heating channel, q0 is the reference value of the heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated vapor, L f is the height of the boiling boundary.

[0127] The friction pressure drop is also divided into single-phase and two-phase regions. The pressure drop of the channel inlet and outlet is also included in the friction pressure drop. The friction pressure drop ΔP f The expression is as follows:

[0128]

[0129] In the formula,

[0130]

[0131] In the formula, f SP is the friction coefficient in the single-phase region, f TS is the friction coefficient of the two-phase region, D e is the diameter of the channel cross section, ρ is the working fluid density, u is the working fluid flow rate, u in is the inlet velocity, u out is the exit speed, u SP is the working fluid flow rate in the single-phase region, ρ out is the outlet density, ρ f is the density of the saturated liquid, k inlet is the form resistance coefficient at the channel entrance, k outlet is the form resistance coefficient of the channel outlet, q0 is the reference value of the heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, A is the cross-sectional area of ​​the non-uniform heating channel, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated steam, L0 is the height of the entire non-uniform heating channel, L f is the height of the boiling boundary.

[0132] For a reactor core with multiple parallel channels, the pressure drop at the inlet and outlet of each channel is equal, that is:

[0133] ΔP tot_1 =ΔP tot_2 =ΔP tot_j =ΔP tot_N

[0134] Where ΔP tot_1 is the total pressure drop in channel 1, ΔP tot_2 is the total pressure drop in channel 2, ΔP tot_j is the total pressure drop in channel j, ΔP tot_N is the total pressure drop of channel N.

[0135] The sum of the flow changes in each channel is equal to the total flow change rate of the core channel. The expression of the total flow change rate of the core channel is as follows:

[0136]

[0137] Where W is the total flow rate of the channel, A j is the cross-sectional area of ​​the jth channel, ρ f is the density of the saturated liquid, u j,in is the inlet velocity of the jth channel, N is the number of parallel channels, and t is the instantaneous time.

[0138] For inter-tube pulsation, the total flow rate remains unchanged. Therefore, by combining the pressure drop relationship of each channel with the unchanged total flow rate, the change rate of the working fluid flow rate at the outlet of each channel can be obtained.

[0139] The pressure drop of each channel is determined by calculating the heat release rate per unit area, and the change rate of the outlet velocity of each channel is determined by using the pressure drop of each channel and the total channel flow rate. Finally, the determined change rate of the outlet velocity of each channel is used to characterize the flow instability in each non-uniform heating channel, which provides a feasible solution for the evaluation of flow instability in non-uniform heating channels in actual operating conditions.

[0140] Optionally, when the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet density, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes:

[0141] determining a rate of change of a saturated liquid channel length based on the expanded non-uniform power distribution;

[0142] The change rate of the outlet density is determined based on the change rate of the saturated liquid channel length, the mass of the working fluid in the single-phase region in the non-uniform heating channel, and the mass of the working fluid in the two-phase region in the non-uniform heating channel.

[0143] Specifically, the total mass M of the coolant in the channel ch The mass M of the coolant in the single-phase region ch_SP and the mass M of the coolant in the two-phase region ch_TP The total mass change rate over time is the sum of the mass change rate in the single-phase region and the mass change rate in the two-phase region. From the continuity equation, the expression of the total mass change rate in the channel is as follows:

[0144]

[0145] Where M ch is the total mass of the coolant in the channel, M ch_SP is the mass of coolant in the single-phase region, M ch_TP is the mass of the coolant in the two-phase region, A is the cross-sectional area of ​​the non-uniform heating channel, ρ f is the density of the saturated liquid, u in is the inlet velocity, u out is the outlet velocity, ρ out is the outlet density, and t is the instantaneous time.

[0146] Mass is the product of density and volume. According to the density formula of the two-phase working fluid, the mass M of the coolant in the two-phase region can be obtained: ch_TP The expression is as follows:

[0147]

[0148] Where A is the cross-sectional area of ​​the non-uniform heating channel, L0 / 2-L f is the height of the two-phase region, v f is the specific volume of the saturated liquid, v fg is the difference between the specific volume of saturated liquid and the specific volume of saturated vapor, h fg is the difference between the enthalpy of saturated liquid and the enthalpy of saturated vapor, h out is the outlet enthalpy, h f is the saturation enthalpy, ρ f is the density of the saturated liquid, ρ out is the export density.

[0149] The working fluid density in the single-phase region can be regarded as the density of the saturated liquid ρ f According to the density of the working fluid in the single-phase region, the mass M of the coolant in the single-phase region can be obtained. ch_SP The expression is as follows:

[0150] M ch_SP =Aρ f (L f +L0 / 2)

[0151] Where A is the cross-sectional area of ​​the non-uniform heating channel, L0 / 2+L f is the height of the single-phase region, ρ f is the density of the saturated liquid.

[0152] Combining the continuity equation, the total mass change rate formula in the channel, the mass formula in the two-phase region, and the mass formula in the single-phase region, the expression for the change rate of the density at the channel outlet is as follows:

[0153]

[0154] In the formula, ρ f is the density of the saturated liquid, u in is the inlet velocity, u out is the outlet velocity, ρ out is the outlet density, L0 / 2-L f is the height of the two-phase region, dL f / dt is the rate of change of the saturated liquid channel length, and t is the instantaneous time.

[0155] The rate of change of the saturated liquid channel length is equivalent to the rate of change of the boiling boundary. The rate of change of the boiling boundary can be determined based on the expanded non-uniform power distribution, that is, the heat release rate per unit area. The algorithm for the rate of change of the boiling boundary has been explained in the previous article and will not be repeated here.

[0156] The rate of change of the saturated liquid channel length is determined by using the heat release rate per unit area, and then the rate of change of the saturated liquid channel length, the mass of the working fluid in the single-phase region of the non-uniform heating channel, and the mass of the working fluid in the two-phase region of the non-uniform heating channel are used to determine the rate of change of the outlet density. Finally, the determined rate of change of the outlet density is used to characterize the flow instability in each non-uniform heating channel, which provides a feasible solution for evaluating the flow instability in the non-uniform heating channel under actual operating conditions.

[0157] The method for determining flow instability in a non-uniform heating channel provided by the present invention can analyze the flow instability in any non-uniform heating channel by Fourier expansion of any heat source based on a triangular basis function and based on a series of mathematical derivations, thereby broadening the application of uniform flow models in the analysis of flow instability in non-uniform heating channels.

[0158] Figure 3 is a schematic diagram of the structure of a device for determining flow instability in a non-uniform heating channel provided by an embodiment of the present invention. Figure 3 As shown, the present invention also provides a device for determining flow instability in a non-uniform heating channel, comprising: a development module 301 and a determination module 302, wherein:

[0159] The expansion module 301 is used to perform Fourier expansion of the non-uniform power distribution based on a triangular basis function.

[0160] The determination module 302 is used to determine flow instability in the non-uniform heating channel based on the non-uniform power distribution after expansion.

[0161] Specifically, the device for determining flow instability in a non-uniform heating channel provided in the embodiment of the present application can implement all the method steps implemented in the above-mentioned method embodiment, and can achieve the same technical effect. The parts and beneficial effects of this embodiment that are the same as those in the method embodiment will not be described in detail here.

[0162] The flow instability determination device in the non-uniform heating channel in the embodiment of the present application can be a device, or a component, an integrated circuit, or a chip in a terminal. The device can be a mobile electronic device or a non-mobile electronic device. Exemplarily, the mobile electronic device can be a mobile phone, a tablet computer, a laptop computer, a PDA, an in-vehicle electronic device, a wearable device, an ultra-mobile personal computer (ultra-mobile personal computer, UMPC), a netbook or a personal digital assistant (personal digital assistant, PDA), etc., and the non-mobile electronic device can be a server, a network attached storage (Network Attached Storage, NAS), a personal computer (personal computer, PC), a television (television, TV), a teller machine or a self-service machine, etc., and the embodiment of the present application is not specifically limited.

[0163] The device for determining flow instability in a non-uniform heating channel in the embodiment of the present application may be a device having an operating system. The operating system may be an Android operating system, an iOS operating system, or other possible operating systems, which are not specifically limited in the embodiment of the present application.

[0164] Figure 4 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention, such as Figure 4 As shown, the electronic device may include: a processor 410, a communication interface 420, a memory 430 and a communication bus 440, wherein the processor 410, the communication interface 420 and the memory 430 communicate with each other through the communication bus 440. The processor 410 may call the logic instructions in the memory 430 to execute the method for determining flow instability in the non-uniform heating channel, based on the one-dimensional uniform flow model, the method includes:

[0165] The non-uniform power distribution is based on the Fourier expansion of triangular basis functions;

[0166] Flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion.

[0167] In addition, the logic instructions in the above-mentioned memory 430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program codes.

[0168] On the other hand, the present invention further provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, when the program instructions are executed by a computer, the computer can execute the method for determining flow instability in a non-uniform heating channel provided by the above methods, based on a one-dimensional uniform flow model, the method comprising:

[0169] The non-uniform power distribution is based on the Fourier expansion of triangular basis functions;

[0170] Flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion.

[0171] In another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon, which is implemented when the computer program is executed by a processor to perform the above-mentioned method for determining flow instability in a non-uniform heating channel, based on a one-dimensional uniform flow model, the method comprising:

[0172] The non-uniform power distribution is based on the Fourier expansion of triangular basis functions;

[0173] Flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion.

[0174] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0175] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0176] In the embodiments of the present application, the terms "first", "second", etc. are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first" and "second" are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining flow instability in a non-uniform heating channel, characterized in that: Based on the one-dimensional uniform flow model, including: The non-uniform power distribution is based on the Fourier expansion of triangular basis functions; determining flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution; The flow instability in the non-uniform heating channel is characterized by one or more of a rate of change of the boiling boundary, a rate of change of the outlet velocity, or a rate of change of the outlet density; In the case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the boiling boundary, the flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion, including: Determine the heat release of the non-uniform heating channel section based on the non-uniform power distribution after expansion; The rate of change of the boiling boundary is determined based on the heat release of the non-uniform heating channel section and the enthalpy value in the single-phase region control body; The total heat release from the inlet to the height L along the axial direction is determined according to the heat release rate per unit area. The expression of the total heat release from the inlet to the height L along the axial direction is as follows: In the formula, q tot (L) is the total heat release from the inlet -L0 / 2 to the height L, U h is the cross-sectional perimeter of the non-uniform heating channel, q0 is the reference value of the heat release rate per unit area, z is the axial height of the channel, and L0 is the height of the entire non-uniform heating channel; According to the total heat release from the inlet to the height L along the axial direction, the n-1 To height L n The heat release of the interval section, from the height L n-1 To height L n The expression of heat release in the interval is as follows: Where q0 is the reference value of heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, L n-1 is the height of the n-1th section of the channel interval, L n is the height of the nth segment of the channel interval, and the subscript n is the number of segments in the channel interval.

2. The method for determining flow instability in a non-uniform heating channel according to claim 1, characterized in that: In a case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes: The rate of change of the outlet velocity is determined based on the expanded non-uniform power distribution, the working fluid density in the two-phase region in the non-uniform heating channel, and the inlet velocity.

3. The method for determining flow instability in a non-uniform heating channel according to claim 1, characterized in that: In a case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet velocity, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes: Determine the voltage drop of each channel based on the expanded non-uniform power distribution; The change rate of the outlet velocity of each channel is determined based on the pressure drop of each channel and the total channel flow.

4. The method for determining flow instability in a non-uniform heating channel according to claim 1, characterized in that: In a case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the outlet density, determining the flow instability in the non-uniform heating channel based on the expanded non-uniform power distribution includes: determining a rate of change of a saturated liquid channel length based on the expanded non-uniform power distribution; The change rate of the outlet density is determined based on the change rate of the saturated liquid channel length, the mass of the working fluid in the single-phase region in the non-uniform heating channel, and the mass of the working fluid in the two-phase region in the non-uniform heating channel.

5. The method for determining flow instability in a non-uniform heating channel according to claim 1, characterized in that: The enthalpy value in the single-phase region control volume is determined under the condition that the enthalpy value in the single-phase region is linearly distributed.

6. A device for determining flow instability in a non-uniform heating channel, characterized in that: Based on the one-dimensional uniform flow model, including: An expansion module, used for Fourier expansion of non-uniform power distribution based on triangular basis functions; a determination module, configured to determine flow instability in the non-uniform heating channel based on the non-uniform power distribution after expansion; The flow instability in the non-uniform heating channel is characterized by one or more of a rate of change of the boiling boundary, a rate of change of the outlet velocity, or a rate of change of the outlet density; In the case where the flow instability in the non-uniform heating channel is characterized by the rate of change of the boiling boundary, the flow instability in the non-uniform heating channel is determined based on the non-uniform power distribution after expansion, including: Determine the heat release of the non-uniform heating channel section based on the non-uniform power distribution after expansion; The rate of change of the boiling boundary is determined based on the heat release of the non-uniform heating channel section and the enthalpy value in the single-phase region control body; The total heat release from the inlet to the height L along the axial direction is determined according to the heat release rate per unit area. The expression of the total heat release from the inlet to the height L along the axial direction is as follows: In the formula, q tot (L) is the total heat release from the inlet -L0 / 2 to the height L, U h is the cross-sectional perimeter of the non-uniform heating channel, q0 is the reference value of the heat release rate per unit area, z is the axial height of the channel, and L0 is the height of the entire non-uniform heating channel; According to the total heat release from the inlet to the height L along the axial direction, the n-1 To height L n The heat release of the interval section, from the height L n-1 To height L n The expression of heat release in the interval is as follows: Where q0 is the reference value of heat release rate per unit area, U h is the cross-sectional perimeter of the non-uniform heating channel, L0 is the height of the entire non-uniform heating channel, L n-1 is the height of the n-1th section of the channel interval, L n is the height of the nth segment of the channel interval, and the subscript n is the number of segments in the channel interval.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method for determining flow instability in a non-uniform heating channel according to any one of claims 1 to 5 are implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for determining flow instability in a non-uniform heating channel as claimed in any one of claims 1 to 5 are implemented.

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