CN110807167A - Boundary processing method for effectively controlling temperature in natural convection cavity with partition plate - Google Patents
Boundary processing method for effectively controlling temperature in natural convection cavity with partition plate Download PDFInfo
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Abstract
The invention provides a boundary processing method for effectively controlling the temperature in a natural convection cavity with a partition plate. Before the constant-temperature bottom plate is heated, the method of the invention is adopted to perform local pulse heating on the bottom plate at intervals to control the alternate appearance of the cold and hot cavities of the system; by the boundary control method, a high-efficiency heat transport channel with alternately distributed cold and heat can be effectively formed in the system.
Description
Technical Field
The invention relates to the field of heat convection heat transfer, in particular to a boundary processing method for effectively controlling the temperature in a natural convection cavity with a partition plate.
Background
As shown in figure 1, the temperature field of the buoyancy convection system with the partition plate is constant-temperature heated at the bottom plate and cooled at the top plate. The white area in the figure represents the heat insulation separation plate, the colored area represents the temperature, a cavity with the overall temperature of almost 0 exists in the system, and the cavity does not contribute to the heat transfer of the system and is not beneficial to the efficient heat transfer of the system.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides a boundary processing method for effectively controlling the temperature in a natural convection cavity with a partition plate. Before the constant-temperature bottom plate is heated, the method of the invention is adopted to perform local pulse heating on the bottom plate at intervals to control the alternate appearance of the cold and hot cavities of the system; by the boundary control method, a high-efficiency heat transport channel with alternately distributed cold and heat can be effectively formed in the system.
In order to solve the problems, the technical scheme of the invention is as follows:
a boundary processing method for effectively controlling the temperature in a natural convection cavity with a partition plate comprises the following steps:
s1, setting a definition variable and an initial value, and starting time step pushing;
defining integer variables includes: pr is 5.3, Pr is the prandtl number and represents the working medium in the system; ra 108Ra is Rayleigh number; number of partitions nj, time step nt, total time step ntm, time step dt equal to 5.0 × 10-4；
Defining floating point type variables including speed V, pressure P, temperature theta, convergence error eps of pressure iteration 1.0 x 10-6(ii) a Where V is (u, V), u is the transverse velocity, V is the longitudinal velocity,
setting an initial value: wherein the speed V, the pressure P, the initial value of the temperature theta are set to be 0, the temperature of the bottom plate is set to be 0.5, and the temperature of the upper plate is set to be-0.5;
s2, adding pulse heating, and carrying out local pulse heating on the constant-temperature heating plate, wherein the heating temperature is twice that of the constant-temperature bottom plate;
s3, decoupling the speed and the pressure by adopting a two-dimensional projection method, and solving the estimated speed V*；
Speed and pressure are decoupled, yielding the following two equations:
in the above equation, k represents a unit vector in the vertical direction, t represents time, and t is nt dt;
using the first equation (1), the estimated velocity V is obtained*；
S4, using the estimated speed V*Solving a pressure Poisson equation to obtain a pressure P;
s5, transforming equation (2) into
According to pressure P and equation
Determining the velocity V of the new time horizon from the pressure and the estimated velocityn+1；
S6, passing the calculated speed V of the new time layern+1And then the energy equation in the N-S equation:
solving the temperature theta of the new time layer through the equation (3) above;
s7, comparing the temperature theta of the layer at the new moment with the temperature at the specific position in the middle of the pulse heating channel, when the theta is larger than a set temperature threshold value, indicating that the pulse heating is enough, removing the pulse heating, and if the theta is smaller than the temperature threshold value, skipping to the step S2 to continue heating;
and S8, continuing to execute the loop until the calculation step number reaches the set total time step number ntm, and ending.
Preferably, the specific implementation process of step S5 is as follows:
the superscript n +1 represents the quantity of the new time layer, the superscript x represents the estimated value, when adopting the format calculation, the partial derivative of t can be changed into the time step dt, the Laplace operator is taken from the two sides of the formula, and the speed satisfies the continuity equation
Thus the above equation is
The equation is a Poisson equation, Gauss Seidel iteration is adopted, namely after a new row of pressure values are iterated each time, the pressure values of the new row are adopted to iterate the pressure of the next row, the iteration speed can be accelerated by the aid of the processing, and in addition, a jump point method is introduced to accelerate convergence of calculation; when the iteration is wrongAnd when the difference is less than the set eps, ending the iteration to obtain P.
Preferably, the selection manner of the temperature threshold in step S7 is as follows: since the dimensionless temperature in the high temperature channel is usually between 0.2-0.5, and the system only needs a small temperature drift in the hot channel to finally form a stable alternating flow of hot and cold, the temperature drift is considered sufficient only when the temperature is greater than 0.0001-0.001.
Preferably, in the step S2, the pulse heating means heating the lower constant temperature heating soleplate at selected intervals.
Compared with the prior art, the invention has the beneficial effects that: in order to overcome the problems in the prior art, before the constant-temperature bottom plate is heated, local pulse heating can be carried out on the bottom plate at intervals, and the cold and hot cavities of the system are controlled to alternately appear. Finally, the feasibility of the method is tested by adopting Direct Numerical Simulation (DNS).
Drawings
FIG. 1(a) is a schematic diagram showing the results of no pretreatment; fig. 1(b) is a schematic diagram showing the result of the boundary processing.
Fig. 2 is a flow chart of the present invention.
FIG. 3 is a schematic view of the addition of a pulsed heating zone.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
Under the assumption of boussinesq, the computational equation of the dimensionless two-dimensional RB thermal convection is
Wherein V is velocity, P is pressure, theta is temperature, dimensionless parameter Ra in the equation is Rayleigh number, and Pr is Plantt number. The boundary conditions were calculated for the lower plate being heated, the dimensionless temperature θ being 0.5, the upper plate being cooled, the dimensionless temperature θ being-0.5. The speed boundary condition is no slip boundary, and the left and right side walls are heat insulation boundaries. The common staggered grid is adopted, the finite difference method is adopted for calculation, the first-order precision is adopted in the time direction, and the second-order precision discrete format is adopted in the space. In this study, the horizontal grids are equidistant, the vertical grids are non-equidistant due to the boundary layer and flow calculation requirements in the slit, and the number of grids is 2000 × 450.
As in fig. 2, a complete description of the calculation process:
the numerical simulation is realized by Fortran language programming, the post-processing drawing adopts a technic tool, the variable name in the invention can be freely defined, and the data related to the calculation process are dimensionless quantities.
1) Variable definition and initial value setting:
the calculation of Fortran requires the definition of data types for all variables involved, for example, integer variables (integer) mainly include: pr is 5.3, Ra is 108The number of partitions nj, the time step nt, the total time step ntm, the time step dt being 5.0 × 10-4. The floating point type variable (real) mainly includes the transverse velocity u, the longitudinal velocity v, the pressure P, the estimated velocity u, the estimated longitudinal velocity v, the temperature θ, and the convergence error eps of the pressure iteration 1.0 × 10-6
Setting an initial value: the velocity u, v, pressure P, temperature θ, etc. are two-dimensional arrays, with an initial value of 0, the soleplate temperature of 0.5, and the upper plate temperature of-0.5.
2) When the time step advances, a loop do while (nt.e. ntm) (le represents less than or equal to) is executed all the time when the time step number is less than the set step number, and the step number is increased by one every time the loop is executed.
3) Adding pulse heating
In the lower thermostatically heated soleplate, spaced selected channels heat. If there are 8 partitions in the system, the system will be divided into 9 channels, and the heating is performed in the region of the bottom plate corresponding to the 1 st, 3 rd, 5 th, 7 th, 9 th or 2 nd, 4 th, 6 th, 8 th channel, as shown in fig. 3.
The heating zone is a 10 grid size zone in the middle of the bottom of the channel, with a dimensionless length of 0.01 and an overall lateral width of 1/200, and the heating is twice the temperature of the base plate.
4) Decoupling speed and pressure by two-dimensional projection method to obtain estimated speed V*＝(u*，v*)；
Speed and pressure are decoupled, and the following two equations can be obtained:
using the first equation, the estimated velocities u, v can be found
Equation of equationNamely, it isThe superscript n +1 represents the quantity of the new time layer, the superscript x represents the estimated value, the Laplace operator is taken from the formula on two sides, and the velocity satisfies the continuity equation
Thus the above formula can be changed intoThe equation is a Poisson equation, in the computational fluid dynamics, a plurality of methods are provided for solving the Poisson equation, for example, a fast Fourier transform is adopted for direct solution, or a relaxation iteration method is adopted, the Gaussian Seidel iteration is adopted in the invention, namely after one new column of pressure values is iterated each time, the pressure values of a new column are adopted for iterating the pressure of the next column, the iteration can be accelerated by the processingAnd in addition, a jumping point method is introduced to accelerate the convergence of calculation. (since these are conventional methods, they are not developed)
5) The pressure can be determined from the above steps and thenThe velocity V of the new time layer can be obtained from the pressure and the estimated velocityn+1。
By the calculated speed V of the new time layern+1And then the energy equation in the N-S equation:
the temperature θ of the new time horizon can be determined from the velocity by the above equation.
6) And judging the temperature at the specific position in the middle of the channel subjected to pulse heating by adding a judgment statement in the program based on the obtained new moment temperature theta, wherein when the temperature is higher than a temperature threshold value, the pulse heating is enough, the pulse heating can be removed, and if the temperature is lower than the temperature threshold value, the pulse heating still needs to be continued.
Selecting a temperature threshold: since the dimensionless temperature in the high temperature channel is usually between 0.2-0.5, and the system only needs a small temperature drift in the hot channel to form a stable alternating flow of cold and hot, the temperature drift can be considered sufficient only when the temperature is greater than 0.0001-0.001.
Measuring a temperature point: how to select a proper position in the channel for temperature judgment is also an important problem, multiple simulation results are comprehensively considered, the measuring point is selected as the middle position of all the channels, the height is the position at the system height 1/4, and when the temperature of all the measuring points is greater than the temperature threshold value, the pulse heating can be removed.
And in the process of time advancing, continuously carrying out pulse heating until the condition in the step 8 is met, and continuously executing circulation until the calculation step number reaches the set size.
Fig. 1(a) is a schematic diagram of the result of no pretreatment, and there is a cavity with an overall temperature of almost 0, which does not contribute to the heat transfer of the system and is not beneficial to the efficient heat transfer of the system. Fig. 1(b) is a schematic diagram of the result after performing boundary processing, and it can be seen from the result in the figure that a high-efficiency heat transport channel with alternately distributed cold and heat can be effectively formed in the system by the boundary control method.
The zero-temperature channel which is not beneficial to efficient heat transfer of the system can randomly appear in experiments and numerical calculation, and the phenomenon can be effectively avoided through boundary control, and the phenomenon also needs to be avoided in engineering practice, so that the popularization of the partition plate system in engineering application is further promoted by the method.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and scope of the present invention shall be included in the protection scope of the claims of the present invention.
Claims (4)
1. A boundary processing method for effectively controlling the temperature in a natural convection cavity with a partition plate is characterized by comprising the following steps:
s1, setting a definition variable and an initial value, and starting time step pushing;
defining integer variables includes: pr is 5.3, Pr is the prandtl number and represents the working medium in the system; ra 108Ra is Rayleigh number; number of partitions nj, time step nt, total time step ntm, time step dt equal to 5.0 × 10-4；
Defining floating point type variables including speed V, pressure P, temperature theta, convergence error eps of pressure iteration 1.0 x 10-6(ii) a Where V is (u, V), u is the transverse velocity, V is the longitudinal velocity,
setting an initial value: wherein the speed V, the pressure P, the initial value of the temperature theta are set to be 0, the temperature of the bottom plate is set to be 0.5, and the temperature of the upper plate is set to be-0.5;
s2, adding pulse heating, and carrying out local pulse heating on the constant-temperature heating plate, wherein the heating temperature is twice that of the constant-temperature bottom plate;
s3, decoupling the speed and the pressure by adopting a two-dimensional projection method, and solving the estimated speed V*；
Speed and pressure are decoupled, yielding the following two equations:
in the above equation, k represents a unit vector in the vertical direction, t represents time, and t is nt dt;
using the first equation (1), the estimated velocity V is obtained*；
S4, using the estimated speed V*Solving a pressure Poisson equation to obtain a pressure P;
s5, transforming equation (2) into
According to pressure P and equation
Determining the velocity V of the new time horizon from the pressure and the estimated velocityn+1；
S6, passing the calculated speed V of the new time layern+1And then the energy equation in the N-S equation:
solving the temperature theta of the new time layer through the equation (3) above;
s7, comparing the temperature theta of the layer at the new moment with the temperature at the specific position in the middle of the pulse heating channel, when the theta is larger than a set temperature threshold value, indicating that the pulse heating is enough, removing the pulse heating, and if the theta is smaller than the temperature threshold value, skipping to the step S2 to continue heating;
and S8, continuing to execute the loop until the calculation step number reaches the set total time step number ntm, and ending.
2. The method according to claim 1, wherein the step S5 is implemented by the following steps:
the superscript n +1 represents the new time horizon quantity, the superscript x represents the estimated value, when using the format calculation, the partial derivative of t can be changed into time step dt, the Laplace operator is taken on the two sides of the equation, and the velocity satisfies the continuity equation ▽. V is 0, so the upper formula is expressed as
The equation is a Poisson equation, Gauss Seidel iteration is adopted, namely after a new row of pressure values are iterated each time, the pressure values of the new row are adopted to iterate the pressure of the next row, the iteration speed can be accelerated by the aid of the processing, and in addition, a jump point method is introduced to accelerate convergence of calculation; and when the iteration error is smaller than the set eps, ending the iteration to obtain P.
3. The method according to claim 2, wherein the temperature threshold in step S7 is selected by: since the dimensionless temperature in the high temperature channel is usually between 0.2-0.5, and the system only needs a small temperature drift in the hot channel to finally form a stable alternating flow of hot and cold, the temperature drift is considered sufficient only when the temperature is greater than 0.0001-0.001.
4. The method of claim 3, wherein in step S2, the heating pulse heating means heating in selected channels spaced in the lower constant temperature heating soleplate.
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