The most important components of electrical vehicles are the battery and the related cooling system. These subsystems play a major role in determining the overall electric vehicle performances. In this study, a novel cooling system with fluid in the battery cell is proposed, by which the energy storage system can be optimized through control of the temperature of the batteries. A sensitivity analysis is conducted considering the maximum temperature, the heat rate, the coolant temperature, and the geometry of the cavities. The numerical simulations show that the parameters for the trapezoidal compartment have an impact on the thermal performance of battery. An optimal geometry is proposed accordingly. It is concluded that for high values of Reynolds number for which the flow becomes turbulent, a decrease in the battery temperature can be obtained thereby avoiding thermal stresses.
Conventional heat exchangers have several basic components. One of these components is a disk or plate that receives heat from a source such as a computer processor. The second component is a set of metal blades that help keep excess heat away from the plate or disc [
Using microfluidic passages that enter directly into the outer shell of the components, researchers at the Georgia Institute of Technology have been able to direct the cooling fluid to where it is most needed for cooling. That is, a few hundred microns away from where the transistors operate. Tests conducted by the Defense Advanced Research Projects Agency (DARPA) have shown that cooling with liquids increases the processing efficiency of the parts by 60% and the average temperature of the parts in this method is about 20 degrees Celsius [
In [
According to the classification of [
In this method, an external force is required to increase heat transfer. Types of active methods include the following: Mechanical auxiliary equipment involves moving the liquid by mechanical equipment or by rotating the surface in a rotary tube exchanger. Surface vibration at high and low frequencies mainly used to increase the heat transfer of a single-phase current.
These methods increase heat transfer by creating turbulence in the flow or changing the flow regime without the need for external force, which is always accompanied by a drop in pressure. Inactive methods include the following: Coated or coated surfaces. These surfaces have metal coatings such as metal particles attached to the surface or non-metallic coatings such as Teflon. It can be seen in the form of samples of coated or coated surfaces. Creating uneven metal coatings on the surface or creating mechanical cavities create steam formation positions on the surface that trap steam inside and turn it into bubbles. Increasing the steam formation positions on the surface increases the core boiling up to 10 times that of the smooth surface. This rough metal coating is created by welding, soldering, flame spraying and electrolytic deposition. In the condensation mode, this method uses Teflon to break the film density to a droplet density, which increases the contact of the vapor with the cold surface and increases the condensing heat transfer. Rough surfaces: The structure of these rough surfaces is generally chosen to disturb the viscous substrate and the purpose of using rough surfaces is not to increase the heat transfer surface (
Modeling of electric vehicle operation with the state of charge of the batteries and its heat transfer is described in
Consider the following differential equation under its boundary conditions to solve φ (x). (
where a and q are known functions in terms of coordinates x, φ_0 and Q_0 are known values and L are one-dimensional domain lengths. The functions a and q and the constants φ_0 and Q_0 along with the amplitude are the problem data. φ is the dependent variable in this problem. When certain values are non-zero, the boundary conditions are called heterogeneous, and when certain values are zero (Q_0 ≠ 0 .φ_0 ≠ 0), the boundary conditions are called homogeneous.
Equations of type 7 appear, for example, in the study of heat conduction in a heat exchanger blade with an axially symmetrical cylinder. It is worth noting that the main purpose of writing the weighted integral expression for the differential equation is to have a tool to obtain n independent linear algebraic relations between the coefficients for the following approximation:
This is made possible by selecting n independent linear weight functions in the integral expression given below. Generating the weak form of any differential equation, if any, has three stages.
These steps are described by the differential equation and the sample boundary conditions. Step 1: All expressions of the differential equation are placed on one side of the equation and the weight function w is multiplied by the whole equation and taken on the amplitude of the integral problem.
The expression
While the expression integral of weight makes it possible to obtain n algebraic relations between C_js for n functions of different arbitrary weights, the functions of the form (approximation) require φ_j to be integral with φ as many as given in the principal differential equation. And satisfy certain boundary conditions. If this does not matter, we can proceed with the integral expression and obtain the necessary algebraic equations for C_j. Approximate methods based on weighted integral expressions are called residual weighted methods. If the derivative is distributed between the approximate solution φ and the weight function w, the resulting integral form requires a weaker coupling condition on φ_j, and hence the expression weighted integral is called the weak form. It will be observed that the formation of weak relationships has two desirable characteristics. First, there is a need for weaker and less consistency for the dependent variable, and it often results in a set of algebraic equations in terms of coefficients. Second, the natural boundary conditions of the problem are included in its weak form, and therefore the approximate solution of φ only needs to satisfy the basic conditions of the problem. These two weakly shaped features play an important role in creating finite element simulations of a problem.
Referring to the phrase integral and integrating will be except for the first part of the phrase.
The relation of integral integration is given in detail in the following relation:
The important part of this step is to identify the two types of natural and fundamental boundary conditions associated with each differential equation. After changing the derivation between the weight function and the variables, in other words, after completing Step 2, all the boundary expressions of the integral relation are checked. Boundary expressions will contain both a weight function and a dependent variable. Weight function coefficients and their derivatives in boundary expressions are called Secondary Variables. Identification of secondary variables at the boundary constitutes natural boundary conditions.
For the current state, the border expression is wa dφ/dx. The coefficients of the weight function are a dφ/dx. Therefore, the secondary variable is a dφ/dx. Secondary variables always have a physical meaning. In the case of heat transfer problems, the secondary variable represents the amount of heat Q. This variable is expressed as follows:
where n_x represents the conductor cosine and is equal to the cosine of the angle between the x-axis and the direction perpendicular to the boundary. For one-dimensional problems, the direction perpendicular to the boundary points is always in line with the length of the slope. So at the left end of the domain is n_x = −1 and at the right end is n_x = + 1.
The dependent variable, just as the weight function appears in the boundary expression, is called the primary variable, and its value on the boundary forms the basic boundary condition. For the case, the dependent function φ is the initial variable and the basic boundary condition will contain a certain value of φ at the boundary points.
It should be noted that the number and shape of the primary and secondary variables depend on the degree of the differential equation. The number of primary and secondary variables are always equal and there is a secondary variable for each primary variable (for example displacement, force, temperature, heat, etc.). Only one condition of the primary and secondary variables can be specified at a point on the boundary. Therefore, in a given problem, certain boundary conditions can be in one of three ways:
All definite boundary conditions are essential.
A number of certain boundary conditions are basic and the rest are natural.
All certain boundary conditions are normal.
For a quadratic equation such as the present problem, there is a primary variable φ and a secondary variable Q. Only one of the two (φ and Q) can be determined at the boundary point. For a quadratic equation, like the classical theory of beams (or Euler-Bernoulli), there are two numbers from each (in other words, two primary variables and two secondary variables). Generally, a 2m degree differential equation has m pairs of primary and secondary variables.
The third and last stage of weak relationships is the application of the real boundary conditions of the problem under consideration. This is where the weight function w at the boundary points, where the basic boundary conditions are set, must be equal to zero. In other words, w must satisfy the homogeneous form of certain basic boundary conditions of the problem.
According to the classification of boundary conditions φ = φ_0, the basic boundary condition and (a dφ/dx) _ (x = L) = Q are natural boundary conditions. Therefore, the weight function w must satisfy the following conditions.
which is a weak form and is equivalent to the initial differential
In the first step, all the expressions of the differential equation are placed on one side (so that the other side of the equation is equal to zero), then the whole equation is multiplied by the weight function and integrated within the problem area. The resulting expression is called the weight integral form of the equation.
In the second stage of integralization, derivation is used separately and derivation is uniformly distributed between the dependent variables and the weight function, and the shape of the primary and secondary variables is determined using boundary expressions.
In the third stage, the boundary expressions are modified by specifying the weight function to satisfy the homogeneous form of certain basic boundary conditions, by substituting secondary variables with their definite values [
Complex functions that are not easily integral can be approximated first with a polynomial and then numerically integrated. If the function is significantly far from linear, then a significant error is expected. But this error can be reduced by increasing the number of partitions between X_0 and X_n. Higher order polynomials can also be used to approximate the function to increase accuracy. In this case, the general form of the integral is:
where n + 1 is the number of sample points.
The polynomials of weight coefficients in
where the values w_i and ξ_i are available for different values of n in the reference [
We begin the discussion by considering the following series of functions:
The above functions are assumed to be acceptable. This means that they meet a series of conditions and have a sufficient degree of continuity. A series of independent functions φ is called linear if the following equation holds:
That is, it must be zero for all α_i. The internal product of φ_1 and φ_2 is defined as follows:
A set of independent linear functions φ_i is called perfect if there are numeric φ values such as n for each arbitrary function and constant coefficients such as α_i, such that the following inequality holds:
where ε is an optional small quantity. In this case, φ_i functions are called base functions and α_i coefficients are called Fourier coefficients. The L operator is defined as a factor that if operates on the function φ, the new function P is obtained as follows:
The L operator is linear if we have:
where α and β are two scalar quantities.
Thermal management of heat generating Li-ion batteries needs a special attention for their better performance, high efficiency, long life and safer operation. The increasing demand for Li-ion batteries in electronic devices and electric vehicles had enticed many researchers to investigate the problems pertinent to overheating of lithium ion batteries which generally occur due to poor thermal management systems.
The thermal performance of the battery model presented in the
Sensitivity analysis of the performance of the EV in with respect to the changes of the hybridization coefficient and determination of the optimum coefficient has been performed, the results of which are presented in
In this section, we define the optimal parameters of a trapezoidal compartment with an N cavity whose geometric characteristics are shown in
In
In the preceding sections, optimization results were obtained to minimize the maximum temperature of the system with the cavity presented in this study for the cavity N. In this section, the minimum temperature of the simplified system presented in this study is compared for the optimal state with the results of the models presented in other studies. In fact, this comparison clearly shows the innovation and performance of the simple model presented in this study. For this purpose, in
Cavity type | φ | α | T(max)_{opt.} | |
---|---|---|---|---|
Reference [ |
C | 0.05 | ∞ | 0.1127 |
Reference [ |
T | 0.05 | ∞ | 0.1017 |
Reference [ |
Y | 0.05 | ∞ | 0.0763 |
Present work | 2-branch | 0.05 | ∞ | 0.0283 |
Present work | 3-branch | 0.05 | ∞ | 0.0126 |
Present work | 4-branch | 0.05 | ∞ | 0.0072 |
Reference [ |
C | 0.1 | ∞ | 0.1008 |
Reference [ |
T | 0.1 | ∞ | 0.071 |
Reference [ |
H | 0.1 | ∞ | 0.0245 |
Present work | 2-branch | 0.1 | ∞ | 0.0253 |
Present work | 3-branch | 0.1 | ∞ | 0.0112 |
Present work | 4-branch | 0.1 | ∞ | 0.0064 |
Reference [ |
C | 0.3 | 0.1 | 61.72 |
Reference [ |
T | 0.3 | 0.1 | 35.5 |
Reference [ |
T-Y | 0.3 | 0.1 | 29.61 |
Reference [ |
T-Y2 | 0.3 | 0.1 | 15.99 |
Present work | 2-branch | 0.3 | 0.1 | 32.67 |
Present work | 3-branch | 0.3 | 0.1 | 22.34 |
Present work | 4-branch | 0.3 | 0.1 | 16.98 |
Present work | 5-branch | 0.3 | 0.1 | 13.7 |
In this section, we present a new system that combines two types of cavities. In this type of system, a cavity with heat transfer displacement accelerates the cooling process, and the other cavity is used by another material with a higher thermal conductivity to distribute the temperature better at the surface of the object. In
Dimensional characteristics of the cavity of the heat exchanger are in accordance with the description of the previous sections. In this section, in order to study the effect of drilling with different conduction resistance, the convexity of the heat transfer surface is considered constant equal to
In
In order to study the effect of conduction coefficient on system performance, in
The performance of modern electric vehicle Li-ion battery cells depends on the working temperature and state of charge variation during the working loads [
The following is suggested for future work in the continuation of the present study:
- Design and optimization of the structure of cooling ducts in electronic components using structural theory
- Structural design for cooling the surface of a disk using streams of materials with high conductivity
- Design and optimization of conductive tree structures in micro and Nano dimensions for cooling electronic components.