Method for calculating deepwater explosion impact resistance of double-sided immersed flexible connection double-layer plate

Abstract

The invention discloses a double-sided immersion flexible connection double-layer plate deepwater explosion impact resistance calculation method, particularly relates to the technical field of underwater explosion impact dynamics, and comprises a compressible multiphase flow calculation method, a fluid-solid coupling calculation method and a structure response calculation method. The motion response of the double-layer plate, the pressure on each fluid-structure interaction surface of the double-layer plate, the external flow field and the interlayer water and the fluid cavitation evolution process in the external flow field and the interlayer water can be calculated.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater explosion impact dynamics, and in particular to a calculation method for deep-water explosion resistance of a double-layer plate with flexible connection and double-sided immersion in water. Background Art

[0002] The combined effects of high hydrostatic pressure and underwater explosion shock loads on underwater vessels are crucial factors affecting their survivability and combat effectiveness. However, existing research methods for underwater vessels subjected to underwater explosion shock loads primarily rely on numerical simulations using commercial software, focusing on single-layer cylindrical shells. Limited research has been conducted on deepwater explosions involving double-layer structures with both sides of the outer shell immersed in water. Existing research on single-shell structures rarely considers the effects of high hydrostatic pressure and under-estimates the generation and collapse of fluid cavitation. For typical double-layer structures of underwater vessels, such as those connected by decking and ribs, the propagation of shock waves and the cavitation process are even more complex, and currently, there is a lack of effective methods to account for these issues in engineering. Summary of the Invention

[0003] In order to overcome the problem that existing underwater explosion calculation methods are unable to quickly and quantitatively evaluate the transmission law of impact loads and the fluid cavitation evolution mechanism in typical double-layer structures of underwater ships connected by decking, side ribs, etc., the present invention proposes a deep-water explosion impact resistance calculation method for double-layer plates with flexible connections on both sides immersed in water. This method can calculate the motion response of the double-layer plates, the pressure on the fluid-solid coupling surfaces of the double-layer plates with the external flow field and the interlayer water, and the fluid cavitation evolution process in the external flow field and the interlayer water, so as to solve the problems raised in the background technology.

[0004] In order to achieve the above object, the present invention provides the following technical solution: a method for calculating the impact resistance of a double-layer plate with flexible connection and double-layer slabs immersed on both sides in water, comprising the following steps:

[0005] Step 1: Set the initial parameters of the double-sided water-immersed double-layer board structure;

[0006] Step 2: Establish the Euler grid domain of the external flow field and interlayer water;

[0007] Step 3: Assigning initial flow field pressure to the flow field according to the underwater explosion shock wave and the hydrostatic pressure field;

[0008] Step 4: Define the initial positions of the three fluid-solid coupling surfaces, namely the outer fluid-outer plate fluid-solid coupling surface, the interlayer water-outer plate fluid-solid coupling surface, and the interlayer water-inner plate fluid-solid coupling surface;

[0009] Step 5: Establish the motion equations of the inner and outer plates, and use Newton's second law to solve the motion of the outer and inner plates;

[0010] Step 6: Determine the stable time step according to the grid sound velocity and the fluid velocity;

[0011] Step 7: For the three fluid-solid coupling interfaces described in step 4, a modified liquid-solid Riemann problem is established based on the state of the grid near the interface and the interface velocity. The modified Riemann problem solver is used to obtain the fluid-solid interface state and assign values ​​to the grid near the interface.

[0012] For the fluid-solid coupling process, it includes the external fluid-external plate fluid-solid coupling surface, the interlayer water-external plate fluid-solid coupling surface, and the interlayer water-inner plate fluid-solid coupling surface. In the fluid-solid coupling solution process, it includes coupling interface capture and solution of fluid and solid states at the interface.

[0013] Step 8: Solve the basic equations of compressible multiphase flow by using the discontinuous Galerkin method to discretize the spatial terms of the Euler equations;

[0014] Step 9: Use the fourth-order Runge-Kutta method to advance the interface Level Set function, perform time discretization on the Euler equation, and perform time discretization on the structural motion equation;

[0015] Step 10: Output the fluid pressure, density, velocity, and structural position and velocity results at the required time;

[0016] Step 11: Repeat steps 6-9 until the calculation time ends.

[0017] Preferably, step 3 is specifically as follows: the underwater explosion shock wave considers a plane shock wave, including the shock wave peak value p0 and the attenuation coefficient θ, and there is also a hydrostatic pressure p in the external flow field. st Assuming that at the beginning of the calculation, the shock wave has been transmitted from the external flow field to the fluid-solid coupling between the external flow field and the outer plate, the pressure distribution in the external flow field is:

[0018]

[0019] Where x is the flow field position, x = 0 is located at the coupling surface between the external flow field and the outer surface of the outer plate, c w is the speed of sound waves in the fluid, t is the time, and the non-reflecting boundary condition is set on the outer boundary of the external flow field.

[0020] Preferably, it is characterized in that: in step 5, the specific structural motion equations of the inner plate and the outer plate are:

[0021]

[0022] Where m1 and m2 are the surface densities of the outer and inner plates, respectively; u1 and u2 are the displacements of the outer and inner plates, respectively. are the accelerations of the outer plate and the inner plate respectively, and p1, p2, and p3 are the pressures of the three fluid-solid coupling surfaces described in step 4, which are solved based on the coupling with the fluid; K CON is the equivalent stiffness of the connection structure, K Sis the inner plate support stiffness; initialize the displacement and velocity of the inner and outer plate structures in equation (2) to 0 in preparation for subsequent solutions.

[0023] Preferably, in step 7, the fluid-solid coupling interface is captured and tracked using the Level Set method, and the specific steps are:

[0024] 1) Establish a level set equation to describe the interface position, and the interface moves at a velocity obtained by calculating the interface state;

[0025] 2) Using the fifth-order precision WENO format to discretize the interface position space, and using the fourth-order precision Runge-Kutta method to discretize the time, the updated distance function is calculated;

[0026] 3) In order to solve the problem that the distance function no longer maintains due to non-uniform flow velocity, the distance function reinitialization equation is established and solved to obtain the corrected distance function;

[0027] 4) Finally, the accurate position of the liquid-solid coupling interface at each time step is obtained;

[0028] Assume that the tracking equation φ(x,t) represents the distance from each grid point to the interface, and the interface tracking Level Set equation is expressed as

[0029]

[0030] Where u = (u, v, w) is the fluid velocity of the Euler grid, and φ(x, t) is transported under non-uniform flow velocity. Non-uniform flow velocity will produce noise characteristics, which will cause the numerical solution φ(x, t) to no longer maintain a distance function. To keep φ(x, t) as a signed distance function, φ(x, t) needs to be reinitialized. The reinitialization equation is:

[0031]

[0032] Where φ0 is the distance function of the Level Set equation at the current time step, S(φ0) is the sign function with appropriate numerical dispersion, τ is the virtual time; the level set equation and the reinitialization equation are solved using the fifth-order weighted essentially non-oscillatory scheme WENO5.

[0033] Preferably, in step 7, the state of the fluid-solid coupling surface is solved using a virtual fluid method, and the specific steps are:

[0034] 1) Based on the position information of the liquid-solid interface and the physical state of the nearby grid, a modified Riemann problem solver between Tait water and the structure is established to obtain the accurate physical state of the fluid-solid coupling interface;

[0035] The state of water is described by the Tait equation of state:

[0036]

[0037] Where ρ0 = 1000 kg / m 3 , A=1.0×10 5 Pa, B = 3.31 × 10 8 Pa,

[0038] 2) Establish an extrapolation equation for the interface state and a high-precision solution method. Using the liquid-solid interface state as input, solve the extrapolation equation to obtain the state of the virtual fluid;

[0039] The corrected Riemann problem solver for the liquid-solid interface is:

[0040]

[0041] The Lagrangian interface velocity obtained from the structural solution is substituted into the liquid-solid Riemann solver as the velocity solution to the Riemann problem established at the interface position. The modified Riemann problem with the known interface velocity is then solved to obtain the interface pressure, which is the pressure p1, p2, and p3 exerted by the fluid-solid coupling surface on the structure.

[0042] Preferably, in step 8, the one-dimensional compressible Euler equation is:

[0043]

[0044] Where t is time, U, F(U) and are the conserved variables, fluxes, and differential operators, respectively;

[0045] During underwater explosions, rarefaction waves are generated due to structural movement. However, the fluid cannot be subjected to tension. When the fluid pressure drops to the critical cavitation pressure, cavitation occurs. As the structure continues to move, the cavitation collapses and re-radiates shock waves. To account for the cavitation effect, the fluid state equation needs to be modified. The isentropic cavitation flow is used to simulate the fluid cavitation process:

[0046]

[0047] Among them, ρ cav For a given cavitation pressure p cav The corresponding density; combined with the fluid isentropic cavitation flow model, the state equation of water is:

[0048]

[0049] Equations (6) and (8) constitute the basic equations for compressible multiphase flow;

[0050] After determining the basic equations, the compressible multiphase flow solution adopts the discontinuous Galerkin method for spatial discretization and the fourth-order Runge-Kutta method for time discretization to form the compressible multiphase flow solution format.

[0051] The present invention has the following advantages:

[0052] The present invention calculates the motion response of the double-layer plate, the pressure on the fluid-solid coupling surfaces of the double-layer plate and the external flow field and interlayer water, and the fluid cavitation evolution process in the external flow field and interlayer water. Compared with the existing technology, the present invention can consider the combined action of hydrostatic pressure and shock waves, solve the double-surface water coupling problem of the outer plate and the cavitation problem of the external flow field and interlayer water, and can quantitatively evaluate the contribution rate of the shock wave transmitted through the interlayer water and through the connecting structure between the inner and outer plates, and can be used to reveal the transmission law of deep-water explosion shock waves in underwater double-hull ships. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A schematic diagram of the double-sided water-immersed flexible connection double-layer board structure provided by the present invention;

[0054] Figure 2 A schematic diagram of the impact response calculation process of a double-layer board with flexible connection and double-sided water immersion provided by the present invention;

[0055] Figure 3 Schematic diagram of pressure results of three fluid-solid coupling surfaces provided by the present invention;

[0056] Figure 4 Schematic diagram of the temporal and spatial distribution of the external flow field and the pressure in the interlayer water provided by the present invention;

[0057] Figure 5 This is a schematic diagram of the movement speed results of the outer plate and inner plate provided by the present invention. DETAILED DESCRIPTION

[0058] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0059] like Figure 2 As shown, this embodiment provides a method for calculating the deep-water explosion impact resistance of a double-layer plate with flexible connection and double-sided water immersion, including the following steps:

[0060] Step 1: Figure 2 As shown, set Figure 1The initial parameters of the double-layer plate structure with double-sided water immersion are shown, including: outer panel surface density m1, inner panel surface density m2, and the equivalent stiffness K of the inner and outer panel connection structure. CON , inner plate support stiffness K S , the thickness of the interlayer water between the inner and outer panels is L CON , the length of the flow field is L; the density of the outer panel m1 is 40kg / m 3 , the inner panel surface density m2 is 200kg / m 3 , the equivalent stiffness of the inner and outer plate connection structure K CON 5×10 8 Pa / s, inner plate support stiffness K S 5×10 9 Pa / s, thickness of interlayer water between inner and outer panels L CON Taking the length of the external flow field calculation domain L as 0.5m and 10m as an example, the temporal and spatial distribution results of the external flow field pressure, the pressure results of the three fluid-solid coupling surfaces and the movement speed results of the inner and outer plates are given;

[0061] Step 2: Figure 2 As shown, the fluid Euler grid domain of the external flow field and the interlayer water is established. Specifically, according to the thickness L of the interlayer water between the inner and outer panels CON The number of fluid grids in the interlayer water and the external flow field is set by the length L of the calculation domain of the external flow field; the calculation results are given as an example with the mesh size of 1mm for the external flow field and interlayer water fluid;

[0062] Step 3: Initialize the flow field pressure according to the underwater explosion shock wave and the hydrostatic pressure field. The underwater explosion shock wave considers the plane shock wave, including the shock wave peak p0 and the attenuation coefficient θ. There is also a hydrostatic pressure p in the external flow field. st ; Assume that at the beginning of the calculation, the shock wave has been transmitted from the external flow field to the fluid-solid coupling between the external flow field and the outer plate, such as Figure 1 As shown, the pressure distribution in the external flow field is:

[0063]

[0064] Where x is the flow field position, x = 0 is located at the coupling surface between the external flow field and the outer surface of the outer plate, c w is the speed of sound waves in the fluid, t is time; the non-reflecting boundary condition is set at the outer boundary of the external flow field; with p0 = 15 MPa, θ = 1.5 ms, p st =1MPa as an example to give the calculation results;

[0065] Step 4: Define the initial positions of the three fluid-structure coupling surfaces, specifically defining the Level Set function of the outer flow field-outer plate interface, the Level Set function of the interlayer water-outer plate interface, and the Level Set function of the interlayer water-inner plate interface;

[0066] Step 5: Figure 2 As shown, the motion equations of the inner and outer plates are established, and the motion of the outer and inner plates is solved using Newton's second law. The specific structural motion equations are:

[0067]

[0068] Where m1 and m2 are the surface densities of the outer and inner plates, respectively; u1 and u2 are the displacements of the outer and inner plates, respectively. are the accelerations of the outer plate and the inner plate respectively, and p1, p2 and p3 are the pressures of the three fluid-solid coupling surfaces respectively, which are solved according to the coupling with the fluid; K CON is the equivalent stiffness of the connection structure, K S is the inner plate support stiffness. Initialize the displacement and velocity of the inner and outer plate structures in equation (2) to 0 in preparation for subsequent solutions;

[0069] Step 6: Determine the stable time step according to the grid sound velocity and the fluid velocity;

[0070] Step 7: For each fluid-solid coupling interface described in step 4, a modified liquid-solid Riemann problem is established based on the state of the grid near the interface and the interface velocity. The modified Riemann problem solver is used to obtain the interface state and assign values ​​to the grid near the interface.

[0071] Step 8: Solve the basic equations of compressible multiphase flow by using the discontinuous Galerkin method to discretize the spatial terms of equation (3);

[0072] Euler equation:

[0073] Where t is time, U, F(U) and are the conserved variables, fluxes, and differential operators, respectively;

[0074] During underwater explosions, rarefaction waves are generated due to structural movement. However, the fluid cannot be subjected to tension. When the fluid pressure drops to the critical cavitation pressure, cavitation occurs. As the structure continues to move, the cavitation collapses and re-radiates shock waves. To account for the cavitation effect, the fluid state equation needs to be modified. The isentropic cavitation flow is used to simulate the fluid cavitation process:

[0075]

[0076] Where ρcav is the density corresponding to the given cavitation pressure pcav; combined with the fluid isentropic cavitation flow model, the state equation of water is:

[0077]

[0078] Equations (3) and (5) constitute the basic equations for compressible multiphase flow;

[0079] Step 9: Use the fourth-order Runge-Kutta method to advance the interface Level Set function, perform time discretization on equation (2), and perform time discretization on equation (3);

[0080] Step 10: Output the fluid pressure, density, velocity, and structural position and velocity results at the required time;

[0081] Step 11: Repeat steps 6-9 until the calculation time ends;

[0082] Step 12. After the calculation is completed, post-processing work is carried out as needed to draw the flow field response diagram and structural motion diagram; the spatiotemporal distribution results of the external flow field and the pressure in the interlayer water in the example are as follows Figure 4 As shown, the movement speed of the inner and outer plates is as follows Figure 5 shown.

[0083] Preferably, in step 4, let the tracking equation φ(x, t) represent the distance from each grid point to the interface, and the interface tracking Level Set equation is expressed as:

[0084]

[0085] Where u = (u, v, w) is the fluid velocity of the Euler grid, and φ(x, t) is transported under non-uniform flow velocity. Non-uniform flow velocity will produce noise characteristics, which will cause the numerical solution φ(x, t) to no longer maintain a distance function. To keep φ(x, t) as a signed distance function, φ(x, t) needs to be reinitialized. The reinitialization equation is:

[0086]

[0087] Where φ0 is the distance function of the Level Set equation at the current time step, S(φ0) is the sign function with appropriate numerical dispersion, τ is the virtual time; the level set equation and the reinitialization equation are solved using the fifth-order weighted essentially non-oscillatory scheme WENO5.

[0088] Preferably, in step 7, the state of the fluid-solid coupling surface is solved using a virtual fluid method; the specific steps are:

[0089] S71. Based on the position information of the liquid-solid interface and the physical state of the nearby grid, a modified Riemann problem solver between Tait water and the structure is established to obtain the accurate physical state of the fluid-solid coupling interface;

[0090] The state of water is described by the Tait equation of state:

[0091]

[0092] Where ρ0 = 1000 kg / m 3, A=1.0×10 5 Pa, B = 3.31 × 10 8 Pa,

[0093] S72. Establish an extrapolation equation for the interface state and a high-precision solution method, use the liquid-solid interface state as an input condition, solve the extrapolation equation, and obtain the state of the virtual fluid;

[0094] The corrected Riemann problem solver for the liquid-solid interface is:

[0095]

[0096] Substitute the Lagrangian interface velocity of the structure solution into equation (9) as the velocity solution of the Riemann problem established at the interface position, and then solve the modified Riemann problem with known interface velocity to obtain the interface pressure, which is the pressure p1, p2 and p3 exerted by the fluid-structure coupling surface on the structure. The pressure results of the three fluid-structure coupling surfaces in the example are as follows: Figure 3 shown.

[0097] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A calculation method for the deep-water explosion resistance of a double-layer plate with flexible connection and double-sided water immersion, characterized by: The following steps are involved: Step 1: Set the initial parameters of the double-sided water-immersed double-layer board structure; Step 2: Establish the Euler grid domain of the external flow field and interlayer water; Step 3: Assigning initial flow field pressure to the flow field according to the underwater explosion shock wave and the hydrostatic pressure field; Step 4: Define the initial positions of the three fluid-solid coupling surfaces, namely the outer fluid-outer plate fluid-solid coupling surface, the interlayer water-outer plate fluid-solid coupling surface, and the interlayer water-inner plate fluid-solid coupling surface; Step 5: Establish the motion equations of the inner and outer plates, and use Newton's second law to solve the motion of the outer and inner plates; Step 6: Determine the stable time step according to the grid sound velocity and the fluid velocity; Step 7: For the three fluid-solid coupling interfaces described in step 4, a modified liquid-solid Riemann problem is established based on the state of the grid near the interface and the interface velocity. The modified Riemann problem solver is used to obtain the fluid-solid interface state and assign values ​​to the grid near the interface. For the fluid-solid coupling process, it includes the external fluid-external plate fluid-solid coupling surface, the interlayer water-external plate fluid-solid coupling surface, and the interlayer water-inner plate fluid-solid coupling surface. In the fluid-solid coupling solution process, it includes coupling interface capture and solution of fluid and solid states at the interface. Step 8: Solve the basic equations of compressible multiphase flow by using the discontinuous Galerkin method to discretize the spatial terms of the Euler equations; Step 9: Use the fourth-order Runge-Kutta method to advance the interface Level Set function, perform time discretization on the Euler equation, and perform time discretization on the structural motion equation; Step 10: Output the fluid pressure, density, velocity, and structural position and velocity results at the required time; Step 11: Repeat steps 6-9 until the calculation time ends.

2. The method for calculating the impact resistance of double-layer plates with double-sided submerged flexible connections in deep-water explosions according to claim 1 is characterized by: Step 3 is as follows: the underwater explosion shock wave considers a plane shock wave, including the shock wave peak p0 and the attenuation coefficient θ. There is also a hydrostatic pressure p in the external flow field. st Assuming that at the beginning of the calculation, the shock wave has been transmitted from the external flow field to the fluid-solid coupling between the external flow field and the outer plate, the pressure distribution in the external flow field is: Where x is the flow field position, x = 0 is located at the coupling surface between the external flow field and the outer surface of the outer plate, c w is the speed of sound waves in the fluid, t is the time, and the non-reflecting boundary condition is set on the outer boundary of the external flow field.

3. The method for calculating the impact resistance of double-layer plates with flexible double-layer connections immersed on both sides of water according to claim 2 is characterized by: In step 5, the specific structural motion equations for the inner and outer plates are: Where m1 and m2 are the surface densities of the outer and inner plates, respectively; u1 and u2 are the displacements of the outer and inner plates, respectively. are the accelerations of the outer plate and the inner plate respectively, and p1, p2, and p3 are the pressures of the three fluid-solid coupling surfaces described in step 4, which are solved based on the coupling with the fluid; K CON is the equivalent stiffness of the connection structure, K S is the inner plate support stiffness; initialize the displacement and velocity of the inner and outer plate structures in equation (2) to 0 in preparation for subsequent solutions.

4. The method for calculating the impact resistance of deep-water explosion of a double-layer plate with flexible connection on both sides of the plate being submerged in water according to claim 1 is characterized by: In step 7, the fluid-structure interaction interface is tracked using the Level Set method. The specific steps are as follows: 1) Establish a level set equation to describe the interface position, and the interface moves at a velocity obtained by calculating the interface state; 2) Using the fifth-order precision WENO format to discretize the interface position space, and using the fourth-order precision Runge-Kutta method to discretize the time, the updated distance function is calculated; 3) In order to solve the problem that the distance function no longer maintains due to non-uniform flow velocity, the distance function reinitialization equation is established and solved to obtain the corrected distance function; 4) Finally, the accurate position of the liquid-solid coupling interface at each time step is obtained; Assume that the tracking equation φ(x,t) represents the distance from each grid point to the interface, and the interface tracking Level Set equation is expressed as Where u = (u, v, w) is the fluid velocity of the Euler grid, and φ(x, t) is transported under non-uniform flow velocity. Non-uniform flow velocity will produce noise characteristics, which will cause the numerical solution φ(x, t) to no longer maintain a distance function. To keep φ(x, t) as a signed distance function, φ(x, t) needs to be reinitialized. The reinitialization equation is: Where φ0 is the distance function of the Level Set equation at the current time step, S(φ0) is the sign function with appropriate numerical dispersion, τ is the virtual time; the level set equation and the reinitialization equation are solved using the fifth-order weighted essentially non-oscillatory scheme WENO5.

5. The method for calculating the impact resistance of double-layer plates with flexible double-layer connections immersed on both sides of water according to claim 1 is characterized by: In step 7, the state of the fluid-solid coupling surface is solved using the virtual fluid method. The specific steps are as follows: 1) Based on the position information of the liquid-solid interface and the physical state of the nearby grid, a modified Riemann problem solver between Tait water and the structure is established to obtain the accurate physical state of the fluid-solid coupling interface; 2) Establish an extrapolation equation for the interface state and a high-precision solution method. Using the liquid-solid interface state as input, solve the extrapolation equation to obtain the state of the virtual fluid; The corrected Riemann problem solver for the liquid-solid interface is: The Lagrangian interface velocity obtained from the structural solution is substituted into the liquid-solid Riemann solver as the velocity solution to the Riemann problem established at the interface position. The modified Riemann problem with the known interface velocity is then solved to obtain the interface pressure, which is the pressure p1, p2, and p3 exerted by the fluid-solid coupling surface on the structure.

6. The method for calculating the impact resistance of double-layer plates with flexible connections on both sides submerged in water, as claimed in claim 1, is characterized by: In step 8, the one-dimensional compressible Euler equation is: Where t is time, U, F(U) and are the conserved variables, fluxes, and differential operators, respectively; During underwater explosions, rarefaction waves are generated due to structural movement. However, the fluid cannot be subjected to tension. When the fluid pressure drops to the critical cavitation pressure, cavitation occurs. As the structure continues to move, the cavitation collapses and re-radiates shock waves. To account for the cavitation effect, the fluid state equation needs to be modified. The isentropic cavitation flow is used to simulate the fluid cavitation process: Among them, ρ cav For a given cavitation pressure p cav The corresponding density; combined with the fluid isentropic cavitation flow model, the state equation of water is: Equations (6) and (8) constitute the basic equations for compressible multiphase flow; After determining the basic equations, the compressible multiphase flow solution adopts the discontinuous Galerkin method for spatial discretization and the fourth-order Runge-Kutta method for time discretization to form the compressible multiphase flow solution format.

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