Cavitation cavitation erosion and secondary cavitation erosion prediction method based on dynamic grid

Abstract

The invention provides a dynamic grid-based cavitation erosion and secondary cavitation erosion prediction method, and belongs to the technical field of fluid machinery and cavitation flow simulation. The prediction method comprises the following steps: carrying out parameter measurement on a deformed engineering material, selecting a computational domain of the deformed engineering material, and carrying out grid division on the computational domain; determining boundary conditions, gas-liquid phase physical property parameters and a mass transfer rate between liquid and gas caused by cavitation; calculating collapse energy, and performing node movement on the gridded computational domain to simulate damage caused by the collapse energy; according to the method, the fluid volume method is used for capturing a multi-phase interface, the cavitation model is used as the basis, the cavity collapse release impact energy is subjected to prediction calculation and converted into distribution of point-shaped cavitation pits with different depths and radiuses on the surface of the model, and the cavitation distribution is predicted according to the collapse energy. And the cavitation erosion collapse on the surface of the prediction model is more visual and accurate.

Description

Technical Field

[0001] The present disclosure relates to the technical field of fluid machinery and cavitation flow simulation, and in particular to a method for predicting grid cavitation erosion and secondary cavitation erosion based on a dynamic grid. Background Art

[0002] In high-speed fluid machinery, cavitation often occurs in low-pressure areas due to the reduction of local pressure in the fluid domain caused by the high fluid flow rate. After the formation and growth stages, cavitation bubbles will collapse violently. The huge impact force generated in a short period of time during collapse will cause a great impact on the material surface. Under repeated action, the material surface often produces plastic deformation and fatigue shedding, which eventually manifests as point pits in the severe cavitation area. Cavitation bubbles are diffuse. In high-speed flow, cavitation bubbles impact the solid surface and produce a large number of diffuse bubbles, which has a great impact on the accuracy of the multiphase solver. Capturing tiny diffuse bubbles requires a large number of grids, which seriously restricts the need for solution efficiency in research and engineering. Through the coupling of the VOF method and the DPM (Discrete Particle Model) particle model, the Lagrangian method tracking of sub-grid scale cavities can be realized, which effectively improves the solution accuracy. Based on the above research background, it is feasible to simulate the cavity distribution characteristics through numerical calculation methods, and it has good accuracy in time average. Based on this, the study of cavitation caused by cavity collapse is carried out.

[0003] Cavitation has affected the development of industrial production, shipping, aerospace and other fields. The unsteady characteristics of cavitation are the main causes of pressure pulsation, vibration, noise and cavitation in water pumps, turbines, underwater propellers and complex piping systems. When the cavity collapses, liquid particles collide with each other and also with the metal surface, which not only corrodes the material surface, but also generates noise of various frequencies, causing vibration.

[0004] At present, many studies measure the intensity of cavitation on the surface of materials by measuring the energy released after the cavity collapses, and use the principle of energy conservation to infer the area with high probability of cavitation by the energy generated by the collapse. The cavitation intensity is often characterized by the weight loss, volume reduction, number of perforations and surface roughness changes of the material per unit time. The use of surface energy or energy density for prediction is not intuitive enough, and it cannot be directly compared with experimental results. Although the fluid-solid coupling method can be used to analyze the cavitation intensity based on material deformation, its interface coupling is relatively complex, and the required calculation steps are relatively complex. It cannot adapt to the complex industrial equipment structure and efficient computing requirements. Therefore, a new calculation method is needed to predict the dynamic grid. Summary of the invention

[0005] A technical problem to be solved by the present disclosure is that the existing fluid-solid coupling method or the reverse method of generating energy through collapse cannot compare data and the calculation process is also very complicated.

[0006] In order to solve the above technical problems, the present disclosure provides a method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid, which includes:

[0007] S1. Parameters of the deformed engineering material are measured, the calculation domain where the engineering material is deformed is selected and the calculation domain is meshed;

[0008] S2. Determine the boundary conditions, gas-liquid phase physical parameters, and the mass transfer rate between the liquid and gas phases caused by cavitation;

[0009] S3, calculate the collapse energy, and move nodes in the gridded computational domain to simulate the damage caused by the collapse energy;

[0010] The collapse energy is the pressure value that satisfies the deformation of the material within a certain period of time and is calculated by integrating the energy conservation formula;

[0011] S4. Simulate the destructive effect of cavitation according to the collapse energy, and finally predict the distribution of cavitation by moving the grid nodes.

[0012] In some embodiments, the aforementioned dynamic grid-based cavitation erosion and secondary cavitation erosion prediction method, wherein the engineering material parameters in S1 include material characteristic parameters such as Young's modulus, Poisson's ratio, shear stress yield limit, yield pressure, etc.; wherein the accuracy of engineering material deformation is determined by the number of grids.

[0013] In some embodiments, in the aforementioned moving grid-based cavitation erosion and secondary cavitation erosion prediction method, in S2, the fluid volume method is used to determine the phase interface, and the cavitation model is used to predict and calculate the cavitation phenomenon.

[0014] In some embodiments, in the aforementioned method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid, the prediction of cavitation phenomenon includes the prediction of cavitation motion, as shown in the following formula:

[0015] E pot =(p d -p v )·V v (1)

[0016] Among them, E pot is the total pressure released by the cavitation bubble, p d is the environmental pressure, p v is the saturated vapor pressure, V v is the volume of the cavitation bubble;

[0017] According to E pot The material derivative at (t, x) can be used to obtain the instantaneous rate of change of potential energy of the flow field at any time and any position, as shown in the following formula:

[0018]

[0019] Among them, α v is the steam volume fraction, u i is the velocity vector in the i direction, u a is the velocity vector in the direction a, V cell is the unit cell volume, where the right side of Formula 2 is the sum of the energy flux generated by collapse and the inertial energy flux.

[0020] In some embodiments, in the aforementioned method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid, when the value of the inertial energy flux in Formula 3 is zero, the cavitation phenomenon is a collapse phenomenon, and the energy generated by the cavitation at this time is:

[0021]

[0022] in, is the energy released by collapse, and u is the velocity vector.

[0023] In some embodiments, the aforementioned method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid, wherein after the energy released by the cavitation collapse is transferred to the material surface, the time is integrated.

[0024]

[0025] Among them, E t is the time integral of the cavitation energy. The grid is updated according to the typical number of cycles or a certain time interval. According to the relationship between material properties and elastic deformation, the linear relationship between energy conversion and pit volume is obtained as follows:

[0026] E t =βηV pit (6)

[0027] Among them, β is the energy and deformation volume conversion coefficient of different materials, η is the energy absorption rate, V pit is the pit volume;

[0028] Considering the pit as a cone, the mesh deformation depth can be obtained from the cone volume formula:

[0029] H=3V pit / πr 3 (7)

[0030] Where r is the equivalent radius of the cell area.

[0031] In some embodiments, in the aforementioned dynamic mesh-based cavitation erosion and secondary cavitation erosion prediction method, when the engineering material mesh is deformed, the global mesh is stretched and smoothed to ensure accurate calculation of the collapse energy to achieve the effect of simulating cavitation erosion.

[0032] In some embodiments, the aforementioned moving grid-based cavitation erosion and secondary cavitation erosion prediction method uses the Euler-Lagrangian algorithm coupling to scan the cavity environment to accurately simulate cavitation morphologies of different scales.

[0033] In some embodiments, the aforementioned dynamic grid-based cavitation erosion and secondary cavitation erosion prediction method, wherein the cavitation model includes cavitation feature calculation of the multiphase model, material surface collapse energy integral of the energy balance equation, and energy / deformation conversion calculation.

[0034] Through the above technical scheme, the present invention provides a cavitation erosion and secondary cavitation prediction method based on a dynamic grid. The present invention implements the capture of multiphase interfaces with the fluid volume method and is based on the cavitation model, which can accurately capture the cavity distribution position and morphology, and can accurately obtain the destruction range of the collapse energy when calculating the collapse capacity, so as to achieve accurate data collection; using dynamic grid technology, the impact energy released by cavity collapse is predicted and calculated, and converted into different depths and radius distributions of point-like cavitation pits on the model surface, so that the prediction of cavitation collapse on the model surface is more intuitive and accurate. Therefore, in this case, the analysis of material deformation is more accurate, and then the analysis of cavitation intensity is more accurate.

[0035] At the same time, it can also be combined with the Euler-Lagrangian multi-scale model to capture the movement and collapse of small bubbles at the sub-grid scale, and consider the energy generated by the collapse of small bubbles to more accurately predict the cavitation area. In this way, it is possible to avoid capturing all small bubble interfaces and consuming a lot of computing resources. At the same time, it can more perfectly describe the movement behavior of small bubbles, saving experimental computing costs and time, and providing assistance for the cavitation optimization design of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 It is a flow chart of a method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid disclosed in an embodiment of the present disclosure;

[0038] Figure 2 It is a schematic diagram of cavitation occurrence and grid deformation of a cavitation erosion and secondary cavitation prediction method based on a moving grid disclosed in an embodiment of the present disclosure;

[0039] Figure 3 This is a demonstration diagram of the continuous diffusion process of bubbles in the cavitation prediction method of this cavitation erosion and secondary cavitation prediction method based on a dynamic grid. DETAILED DESCRIPTION

[0040] The following is a further detailed description of the embodiments of the present disclosure in conjunction with the accompanying drawings and examples. The detailed description of the following embodiments and the accompanying drawings are used to exemplarily illustrate the principles of the present disclosure, but cannot be used to limit the scope of the present disclosure. The present disclosure can be implemented in many different forms and is not limited to the specific embodiments disclosed herein, but includes all technical solutions that fall within the scope of the claims.

[0041] The present disclosure provides these embodiments to make the present disclosure thorough and complete, and to fully express the scope of the present disclosure to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the parts and steps, the composition of the materials, the numerical expressions and the numerical values ​​set forth in these embodiments should be interpreted as being merely exemplary, and not as limiting.

[0042] It should be noted that, in the description of the present disclosure, unless otherwise specified, the meaning of "multiple" is greater than or equal to two; the terms "upper", "lower", "left", "right", "inner", "outer", etc., indicating the orientation or positional relationship, are only for the convenience of describing the present disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present disclosure. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0043] In addition, the words "first", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different parts. "Vertical" does not mean vertical in the strict sense, but is within the tolerance range. "Parallel" does not mean parallel in the strict sense, but is within the tolerance range. "Include" or "comprising" and similar words mean that the elements before the word include the elements listed after the word, and do not exclude the possibility of including other elements.

[0044] It should also be noted that in the description of the present disclosure, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms in the present disclosure can be understood according to the specific circumstances. When a specific device is described as being located between a first device and a second device, there may or may not be an intermediate device between the specific device and the first device or the second device.

[0045] All terms used in the present disclosure have the same meanings as those understood by those of ordinary skill in the art to which the present disclosure belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries, for example, should be interpreted as having meanings consistent with their meanings in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined as such herein.

[0046] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered part of the specification.

[0047] Embodiment 1

[0048] Reference Figure 1 , this embodiment discloses a cavitation erosion and secondary cavitation erosion prediction method based on a moving grid, comprising the following steps;

[0049] S1. Parameter measurement of deformed engineering materials and meshing of pre-set calculation domains;

[0050] Specifically, after implementing S1, the established material deformation corresponding to the mesh deformation rule is written into the solver through a program as a user-defined function (UDF) code, based on the volume of fluid (VOF) and Schnerr-Sauer (SS) cavitation model. Its transport equation is expressed as:

[0051]

[0052] Among them, ρ v is the gas phase density, ρ l is the liquid density, α is the gas volume fraction, is the gas phase velocity, t is the time, and specifically, the mass transfer rate equation between the gas phase and the liquid phase can be expressed as:

[0053]

[0054] The Schnerr-Sauer model relates the vapor volume fraction to the number of bubbles in each cell using the following expression:

[0055]

[0056] Among them, n b is the bubble number density, is the bubble radius.

[0057] S2. Determine the boundary conditions, gas-liquid phase physical parameters, and the mass transfer rate between the liquid and gas phases caused by cavitation;

[0058] Specifically, S2 uses the fluid volume method to determine the multiphase interface and the cavitation model to predict and calculate the cavitation phenomenon.

[0059] like Figure 2 As shown, after implementing S2, the flow field parameters, the generation, movement and distribution of cavitation are accurately calculated. After its collapse, energy is released to the material surface. The energy received by the material is predicted based on the law of conservation of energy, and the energy size of cavitation is obtained by combining the experimentally obtained material's absorption rate of the collapse energy wave.

[0060] After the energy released by cavitation collapse is transferred to the material surface, it is integrated over time to satisfy Formula 5: For the energy mapped onto the surface, the grid is updated according to the calculated typical number of cycles or a certain time interval. Based on the relationship between material properties and elastic deformation, the linear relationship between energy conversion and pit volume is obtained as follows:

[0061] E t =βηV pit (6)

[0062] Among them, for aluminum, the parameters Energy absorption rate η~0.02v, v is the characteristic flow velocity. Different engineering materials have different deformation parameters. The pit is approximately regarded as a cone, and the grid deformation depth H=3V according to the cone volume formula. pit / πr 3 Among them, r is the equivalent radius of the unit cell area. Finally, combined with the energy generated by cavitation and the volume of the pit, a multiphase calculation model can be established to accurately calculate the flow field, cavitation generation, and the transport and collapse of the cavity. On this basis, the energy of the cavity can be calculated according to the principle of energy conservation, and the energy released by the collapse and its impact on the wall are further discussed.

[0063] Among them, the potential energy of cavity motion is determined by the pressure difference between ambient pressure and saturated vapor pressure, that is, p d -p vThe cavity volume fraction V v The work done is driven by:

[0064] E pot =(p d -p v )·V v (1)

[0065] The first term of formula 1 includes the change in gas phase volume, which will generate an energy flux that induces collapse, converting part of the initial potential energy in the bubble into the initial energy of collapse and distributing it to the flow field around the cavity. The second term mainly describes the change in inertial potential energy of the cavity under the driving pressure. This change in potential energy changes the speed of the cavity movement, so the motion potential energy of the cavity is finally obtained.

[0066] According to E pot The material derivative at (t, x) can be used to obtain the instantaneous rate of change of potential energy of the flow field at any time and any position, which can be expressed as:

[0067]

[0068] in The right side of Formula 2 is the sum of the energy flux generated by collapse and the inertial energy flux. It can be understood that when the inertial energy flux in Formula 2 is zero, all the energy of the cavity is converted into the phase that induces collapse. At this moment, collapse occurs. Considering that the kinetic energy of the cavity is eventually converted into potential energy under a negative pressure gradient, the formula is: The term can describe the energy released by collapse, which is finally expressed as:

[0069]

[0070] like Figure 3 As shown in the figure, the trapezoidal shape on the top is a cavitation nozzle, from which a high-speed cavitation jet is ejected and impacts the metal sample plane at the bottom. The metal sample surface at the bottom is impacted, with a larger impact load in the center and gradually decreasing toward the periphery. Figure 3 The cloud image on the sample surface represents the pressure on its surface. The cloud-like image represents large-scale cavities and cavitation clusters. After development, due to the slow flow rate around the sample and the increase in pressure, their volume shrinks, and they collapse or transform into discrete small bubbles. Figure 3 The process of shrinking and collapsing from large bubbles to small bubbles was directly observed, and the compression of the cavity and the changes in the location and time of collapse and the energy carried by the collapse were explained.

[0071] S3, calculate the collapse energy, and move nodes in the gridded computational domain to simulate the damage caused by the collapse energy;

[0072] Specifically, when the collapse pressure meets the material deformation pressure, the collapse energy transferred to the surface is calculated by integrating the energy conservation formula. After a certain time step or a certain number of cycles, the nodes of the selected "material" grid are moved to simulate the cavitation damage on the material surface. On the other hand, the global grid moves accordingly, and the grid changes caused by cavitation damage are updated in time to make the grid closer to the changes in deformation, so as to meet the needs of calculating the grid quality.

[0073] Among them, the mesh deformation size is determined by the material plastic deformation parameters and formulas, and the derivation process includes:

[0074]

[0075] Where σ is the stress of the material, σ y is the yield strength of the material, and E is the Young's modulus of the material. The yield strength and stress of the material can be calculated by the instantaneous pressure difference and the unit cell area. Deformation will occur only when the instantaneous stress acting on the material surface is greater than the yield strength of the material. It can be understood that the pressure gradient of the cavitation surface at the moment of collapse can be obtained by subtracting the local low-pressure area and the overall pressure of the flow field generated after the collapse. When the pressure gradient is greater than the maximum cavitation pressure of the material, it can be considered that the material has undergone plastic deformation, and the degree of deformation is determined by the area of ​​the material region where the pressure gradient is greater than the yield pressure and the accumulated impact energy on the material surface. The conversion formula used is as follows:

[0076]

[0077] Among them, ΔS is the area of ​​the grid for the calculated deformation, Δt is the interval between two deformations, ∑E is the deformation energy actually received by the pattern, β is the energy absorption proportional coefficient of the material, and V is the energy released to the surface of the material by the collapse predicted by the formula. The energy obtained by the material surface is linearly related to the size of its pit deformation, which can be expressed by formula 6E t =βηV pit , combined with the mesh deformation depth H = 3V pit / πr 3 Calculations are performed where different materials have different energy and deformation volume conversion coefficients.

[0078] S4. The destructive effect of cavitation is simulated according to the collapse energy, and finally the distribution of cavitation is predicted by moving the grid nodes; wherein, when predicting the distribution of cavitation, the Euler-Lagrangian multi-scale model can be used to further capture the cavity, and the energy released by the bubble collapse is predicted at the sub-grid scale to obtain a more refined cavitation distribution. It can be understood that the Euler-Lagrangian cavitation conversion algorithm can convert the continuous bubble volume captured by the fluid volume method into a discrete bubble tracked by the Lagrangian algorithm when the volume is smaller than the cell size, so as to further capture the movement and collapse of the discrete bubbles. Combined with the above method, the collapse effect of the discrete bubbles can be further predicted.

[0079] After S1-S4 is implemented, the mesh quality of the fluid domain meets the requirements for further calculations due to the adoption of mesh smoothing strategies. Figure 2 As shown in the first part, the initial grid is a regular structural grid. As the collapse occurs, the impact energy received is accumulated on its surface. After accumulating to a certain extent, the grid undergoes a corresponding slight deformation and transmits the deformation to the grid slightly further away (such as Figure 2 As shown in the second part), in order to ensure that the mesh quality meets further calculation requirements, the present invention can further predict and accumulate type variables based on the deformed mesh, such as Figure 2 As shown in the third part, after multiple cycles of accumulation, cavitation pits of varying depths are eventually formed on the material surface, thereby achieving the purpose of predicting cavitation behavior, and the influence of the uneven cavitation surface is taken into account in the next cavitation calculation.

[0080] So far, various embodiments of the present disclosure have been described in detail. In order to avoid obscuring the concept of the present disclosure, some details known in the art are not described. Based on the above description, those skilled in the art can fully understand how to implement the technical solution disclosed here.

[0081] Although some specific embodiments of the present disclosure have been described in detail by way of examples, it should be understood by those skilled in the art that the above examples are for illustration only and are not intended to limit the scope of the present disclosure. It should be understood by those skilled in the art that the above embodiments may be modified or some technical features may be replaced by equivalents without departing from the scope and spirit of the present disclosure. In particular, the various technical features mentioned in the various embodiments may be combined in any manner as long as there is no structural conflict.

Claims

1. A method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid, characterized in that: The following steps are involved: S1. Parameters of the deformed engineering material are measured, the calculation domain where the engineering material is deformed is selected and the calculation domain is meshed; S2. Determine the boundary conditions, gas-liquid phase physical parameters, and the mass transfer rate between the liquid and gas phases caused by cavitation; S3, calculate the collapse energy, and move nodes in the gridded computational domain to simulate the damage caused by the collapse energy; The collapse energy is the pressure value that satisfies the deformation of the material within a certain period of time and is calculated by integrating the energy conservation formula; S4. Simulate the destructive effect of cavitation according to the collapse energy, and finally predict the distribution of cavitation by moving the grid nodes.

2. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 1, characterized in that: The engineering material parameters in S1 include material characteristic parameters such as Young's modulus, Poisson's ratio, shear stress yield limit, and yield pressure; Among them, the accuracy of engineering material deformation is determined by the number of grids.

3. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 1, characterized in that: In S2, the fluid volume method is used to determine the multiphase interface, and the cavitation model is used to predict and calculate the cavitation phenomenon.

4. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 3, characterized in that: The prediction of cavitation phenomena includes the prediction of cavitation motion, as shown in the following formula: E pot =(p d -p v )·V v (1) Among them, E pot is the total pressure released by the cavitation bubble, p d is the environmental pressure, p v is the saturated vapor pressure, V v is the volume of the cavitation bubble; According to E pot The material derivative at (t, x) can be used to obtain the instantaneous rate of change of potential energy of the flow field at any time and any position. As shown below: Among them, α v is the steam volume fraction, u i is the velocity vector in the i direction, u a is the velocity vector in the direction a, V cell is the unit cell volume, where the right side of Formula 2 is the sum of the energy flux generated by collapse and the inertial energy flux.

5. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 4, characterized in that: When the value of the inertial energy flux in formula 3 is zero, the cavitation phenomenon is a collapse phenomenon. At this time, the energy generated by cavitation is E pt for: in, is the energy released by collapse, and u is the velocity vector.

6. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 5, characterized in that: After the energy released by cavitation collapse is transferred to the material surface, the time is integrated. Among them, E t is the time integral of the cavitation energy. The grid is updated according to the typical number of cycles or a certain time interval. According to the relationship between material properties and elastic deformation, the linear relationship between energy conversion and pit volume is obtained as follows: E t =βηV pit (6) Among them, β is the energy and deformation volume conversion coefficient of different materials, η is the energy absorption rate, V pit is the pit volume; Considering the pit as a cone, the mesh deformation depth H can be obtained from the cone volume formula: H=3V pit / πr 3 (7) Where r is the equivalent radius of the cell area.

7. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 6, characterized in that: When the engineering material mesh is deformed, the global mesh is stretched and smoothed to ensure accurate calculation of the collapse energy to achieve the effect of simulating cavitation.

8. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 1, characterized in that: The cavity environment is scanned by coupling the Euler-Lagrangian algorithm to accurately simulate the cavitation morphology at different scales.

9. The method for predicting cavitation erosion and secondary cavitation erosion based on a moving grid according to claim 3, characterized in that: The cavitation model includes the calculation of cavitation characteristics of the multiphase model, the material surface collapse energy integral of the energy balance equation, and the energy / deformation conversion calculation.

Images