CN109084952A - Calculation method based on the small-sized supercavitating vehicle vacuole deformation of potential flow theories - Google Patents
Calculation method based on the small-sized supercavitating vehicle vacuole deformation of potential flow theories Download PDFInfo
- Publication number
- CN109084952A CN109084952A CN201810917902.XA CN201810917902A CN109084952A CN 109084952 A CN109084952 A CN 109084952A CN 201810917902 A CN201810917902 A CN 201810917902A CN 109084952 A CN109084952 A CN 109084952A
- Authority
- CN
- China
- Prior art keywords
- vacuole
- sail body
- function
- point
- barrier
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M10/00—Hydrodynamic testing; Arrangements in or on ship-testing tanks or water tunnels
Landscapes
- Physics & Mathematics (AREA)
- Fluid Mechanics (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The invention discloses a kind of calculation methods based on the small-sized supercavitating vehicle vacuole deformation of potential flow theories.It include the following steps: (1) establishment of coordinate system, step 2, complex potential are superimposed, step 3,kWithΔxDetermination, step 4, dynamic pressure field solve, step 5, vacuole deformation solution.The present invention solves in restricted clearance, the computational problem of supercavity form, and the present invention calculates acquired results and test result with high consistency.
Description
Technical field
The present invention relates to the calculation methods of underwater supercavitating vehicle vacuole form, specifically, being one kind in barrier
The calculation method of neighbouring its vacuole of small-sized supercavitating vehicle deformation.
Background technique
Two methods of viscosity flow and potential barrier, M.Lee etc. are mainly used for the theoretical research in supercavitating vehicle movement flow field
Pressure disturbance before sail body is decomposed into transverse pressure and longitudinal pressure using point source method and unsteady Bernoulli equation by people, right
Problem of water entry has carried out calculating analysis.Zhao Chenggong et al. is embedded in CEL sail body equation of motion program, success mould by CFX software
The tail for having intended supercavitating vehicle claps movement, obtains tail and claps the conclusion for destroying vacuole form symmetry.
Underwater supercavitating vehicle is compared with traditional underwater sailing body, because its ship resistance is small so being always to study heat
Point, the vacuole form computational problem in relation to underwater supercavitating vehicle, now focus mostly in two methods of use: slender bodies potential barrier is managed
Equation is independently expanded by with Logvinovich vacuole, and the consistency of two methods and test is preferable, but it is only applicable to infinitely
Big flow field is also not directed to the small-sized sail body vacuole form calculating influenced by barrier, therefore, in order to study underwater vacuole
By the form of obstacle-produced turbulence, by the empty image point source method of hydrodynamics potential flow theories, in conjunction with Bernoulli equation and
Logvinovich vacuole independently expands equation, carries out theoretical calculation to vacuole model deformation, mentions for research sail body unstable phenomenon
For calculation basis.
Summary of the invention
The purpose of the present invention is to propose to one kind, and based on the small-sized supercavitating vehicle of potential flow theories, the vacuole near barrier becomes
The calculation method of shape.
Realize technical solution of the invention are as follows: a kind of based on potential flow theories small-sized supercavitating vehicle vacuole deformation
Calculation method, which comprises the following steps:
Step 1, establishment of coordinate system: establishing plane complex coordinates system on two-dimensional surface, and takes sail body coordinate points and about y
Position of the mirror point coordinate of axis as point source and its empty image point source, according to sail body movement velocity changing rule in water,
Establish the functional relation that coordinate points change over time；
Step 2, complex potential superposition: according to the complex potential Function Solution of hydrodynamics basic flowing, on a complex plane to point source and
The complex potential of its empty image point source is overlapped, and abbreviation is complex function form；
The determination of step 3, k and Δ x: on the motion profile of sail body, one navigation body length of selected distance barrier
L takes any step delta x (Δ x < < L), then k=L/ Δ x, and L is carried out k equal part.
Step 4, dynamic pressure field solve: meaning and analytical function Cauchy-Riemann based on hydrodynamics potential function and stream function
Formula solves moving source on its motion profile, and equidistant in front of barrier (speed changes over time at the k point of Δ x)
Functional relation, and defined by dynamic pressure and to acquire dynamic pressure on k point and change with time relationship Pdk(t)；
Step 5, vacuole deformation solution: be averaged to the dynamic pressure at equidistant k point in front of barrier, and by mean value
It brings into the pressure term of Logvinovich equation, Logvinovich equation is solved with complexification Simpson method, thus
Obtain vacuole form.
Compared with prior art, the present invention its remarkable advantage are as follows: 1) present invention solves in restricted clearance, supercavity shape
The computational problem of state.2) present invention can obtain the numerical result of the vacuole local radius after by obstacle-produced turbulence.3) present invention meter
Calculating acquired results and test result has high consistency.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart
Fig. 2 is the method for the present invention void image point-source model figure.
Fig. 3 is that the method for the present invention vacuole is schemed by dynamic pressure disturbance.
Fig. 4 is the method for the present invention calculate node dynamic pressure changing rule.
Fig. 5 is the method for the present invention sail body displacement time curve.
Fig. 6 is the selection figure of the method for the present invention example calculation node.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
In conjunction with Fig. 1:
Step 1, establishment of coordinate system: such as Fig. 2, if sail body head is a at a distance from barrier, with sail body motion profile
For x-axis, the intersection with barrier is coordinate origin, and barrier is y-axis, establishes complex number plane z.According to empty image point source method
Sail body is made mirror image to y-axis by equivalent rule, and mirror image point source is-a, and a is the function of time
Wherein X0It is to calculate initial time sail body at a distance from barrier, the movement velocity of V (τ) sail body is at any time
Change function, tbIt, can be by for sail body hours underway
It integrates
Wherein V0For sail body initial velocity, m is navigation weight, ρwFor water density, A0For sail body cavitation device sectional area, Cd
Taking 0.82, V for resistance coefficient is sail body instantaneous velocity.
Step 2, complex potential superposition: for point source basic flowing its be located at complex plane z0Place, reset on a complex plane
Gesture are as follows:
Wherein Q is the flow at point source, and ξ=Q/2 π is source strength.
Positioned at A (a, 0), the complex potential superpositing function of two point sources generation of B (- a, 0) are as follows:
W (z)=ξ ln (z-a)+ξ ln (z+a)
WhereinFor potential function, ψ is stream function, and both ends of the equation takes logarithm to obtain:
E is unfolded with Euler formulaiψ:
That is:
To above two formula both sides square and it is added and takes logarithm and ratio is made to upper two formula and its inverse function is asked to be in power respectively letter
NumberWith stream function ψ expression formula are as follows:
The determination of step 3, k and Δ x: on the motion profile of sail body, one navigation body length of selected distance barrier
L takes any step delta x (Δ x < < L), then k=L/ Δ x, and L is carried out k equal part.
Step 4, dynamic pressure field solve: stream functionWith potential function ψ expression formula are as follows:
Had by complex function parsing property Cauchy-Riemann condition:
Because stream function has more compact form than potential function, the determination of source strength, root are avoided to a certain extent
According to the definition of Cauchy-Riemann condition and potential function ψ, stream functionAsk partial derivative that can solve on two-dimensional surface x, y respectively
The velocity component function of any is put how general caused by source movement since the movement velocity of point source is far smaller than the underwater velocity of sound
Strangling effect can be ignored, preferable by the consistency for calculating its result and test, show that ignoring Doppler effect here is
It is feasible.
Wherein u is the fluid velocity in the direction x, and v is the fluid velocity in the direction y.
It can be seen from the above result that fluid velocity is unrelated with source strength, so certain position before the target as caused by source movement
Hydrodynamic (such as Fig. 3) are as follows:
Wherein Pd(t) strong for hydrodynamic.
Thus, equidistant in front of barrier (functional relation that speed changes over time at the k point of Δ x), and by moving
Pressure definition acquires dynamic pressure on k point and changes with time relationship Pdk(t)；
Step 5, vacuole deformation solution: fluid be it is incompressible have a potential barrier, consider the feelings that sail body moves along a straight line under water
Condition, sail body is with initial velocity V∞Movement, and decay according to inverse proportion function rule.If saturated vapor pressure is p inside vacuolev,
Outside pressure is p, and Logvinovich derives that the vacuole based on potential flow theories independently expands equation according to energy conservation equation:
Wherein, k is that coefficient is faint dependent on cavitation number σ=Δ p/ (0.5 ρ v2), usually take k=4 π/(A2), A ≈ 2 is warp
Test constant.
Outside pressure p is infinite point pressure in infinite space, and for the confined space before target, vacuole is by dynamic pressure shadow
Pilot causes vacuole deformation that diameter contracting occurs, and generates in superposition on the infinite point pressure p of infinite space because of local space disturbance
Hydrodynamic, i.e. p=p∞+Pd(t), wherein infinite point pressure p∞=p0+ ρ gh, h are depth under water where supercavity bullet, p0
For atmospheric pressure, ρ is the density of water, and g is acceleration of gravity, PdIt (t) is the pressure mean value on k node
Discrete solution is carried out to Logvinovich equation with complexification Simpson method, to obtain vacuole form.
It is described in more detail below with reference to embodiment.
It is 2m, initial velocity 200m/s for keel depth, apart from barrier 2m, certain small-sized sail body is calculated,
Take Δ x=18mm, k=6, L=110mm.Fig. 4 is that gained testing site dynamic pressure curve is calculated using empty image point source method,
Initial time due to sail body apart from node A, B, C, D, E, F farther out, do not generate dynamic pressure at 6 nodes, work as t=0.009s
When, F point generates dynamic pressure disturbance at first, and sail body moving displacement is 1.6m (such as Fig. 5) at this time, and E, D, C, B, A point are sequentially generated dynamic
Pressure, occur pressure peak successively increases and accompanying event lag the phenomenon that.The last one moment point of dynamic pressure curve, is navigated by water at this time
Body touches barrier, and the dynamic pressure highest of A point, this tallies with the actual situation.The dynamic pressure value of disturbance chooses the last one
The dynamic pressure mean value of 6 nodes of moment, tallies with the actual situation in this way from the point of view of calculated result.
Table 1 provides the computable value with test value of corresponding node disturbance front and back vacuole diameter, it can be seen that test value and calculating
The consistency of value is preferable, illustrates that the deformation of vacuole form before the empty image point source method of potential flow theories can be used for calculating barrier is asked
Topic illustrates that the metaboly of vacuole before barrier is that sail body movement causes fluid and obstacle effect to generate the comprehensive of dynamic pressure to imitate
Fruit.
The computable value with test value comparison of 1 corresponding node of table disturbance front and back vacuole diameter
Claims (5)
1. a kind of calculation method based on the small-sized supercavitating vehicle vacuole deformation of potential flow theories, which is characterized in that including following
Step:
Step 1, establishment of coordinate system: establishing plane complex coordinates system on two-dimensional surface, and takes sail body coordinate points and about y-axis
Position of the mirror point coordinate as point source and its empty image point source is established according to sail body movement velocity changing rule in water
The functional relation that coordinate points change over time；
Step 2, complex potential superposition: according to the complex potential Function Solution of hydrodynamics basic flowing, on a complex plane to point source and its void
The complex potential of image point source is overlapped, and abbreviation is complex function form；
The determination of step 3, k and Δ x: on the motion profile of sail body, one navigation body length L of selected distance barrier is taken
Any step delta x, Δ x < < L, then k=L/ Δ x, carries out k equal part for L；
Step 4, dynamic pressure field solve: meaning and analytical function Cauchy-Riemann formula based on hydrodynamics potential function and stream function,
Moving source is solved on its motion profile, equidistant in front of barrier (function that speed changes over time at the k point of Δ x) closes
System, and defined by dynamic pressure and to acquire dynamic pressure on k point and change with time relationship Pdk(t)；
The solution that step 5, vacuole deform: it is averaged to the dynamic pressure at k point equidistant in front of barrier, and mean value is brought into
In the pressure term of Logvinovich equation, Logvinovich equation is solved with complexification Simpson method, to obtain
Vacuole form.
2. calculation method according to claim 1, it is characterised in that: establishment of coordinate system described in step 1:
If sail body head is a at a distance from barrier, using sail body motion profile as x-axis, the intersection with barrier is to sit
Origin is marked, barrier is y-axis, establishes complex number plane z；According to the equivalent rule of empty image point source method, sail body is made into mirror to y-axis
Picture, mirror image point source is-a, and a is the function of time
Wherein X0To calculate initial time sail body at a distance from barrier, the movement velocity of V (τ) sail body changes with time
Function, tbFor sail body hours underway, by
It integrates
Wherein V0Initial velocity is calculated for sail body, m is navigation weight, ρwFor water density, A0For sail body cavitation device sectional area, CdFor
It is sail body instantaneous velocity that resistance coefficient, which takes 0.82, V,.
3. calculation method according to claim 1, it is characterised in that: the superposition of complex potential described in step 2:
Positioned at A (a, 0), the complex potential superpositing function of two point sources generation of B (- a, 0) are as follows:
ξ=Q/2 π is source strength, and Q is the flow at point source；
Potential functionWith stream function ψ expression formula are as follows:
4. calculation method according to claim 1, it is characterised in that: dynamic pressure field described in step 4 solves:
, certain position hydrodynamic before the target as caused by source movement are as follows:
Wherein Pd(t) strong for hydrodynamic；
Thus, equidistant in front of barrier (functional relation that speed changes over time at the k point of Δ x), and determined by dynamic pressure
Justice acquires dynamic pressure on k point and changes with time relationship Pdk(t)。
5. calculation method according to claim 1, it is characterised in that: the solution of the deformation of vacuole described in step 5:
Logvinovich derives that the vacuole based on potential flow theories independently expands equation according to energy conservation equation:
Wherein, k is that coefficient is faint dependent on cavitation number σ=Δ p/ (0.5 ρ v2), take k=4 π/(A2), A ≈ 2 is empirical, empty
Steeping internal saturated vapor pressure is pv, outside pressure p；
P=p∞+Pd(t), wherein infinite point pressure p∞=p0+ ρ gh, h are depth under water where supercavity bullet, p0For atmosphere
Pressure, ρ are the density of water, and g is acceleration of gravity, PdIt (t) is the pressure mean value on k nodeWith again
Change Simpson method and discrete solution is carried out to Logvinovich equation, to obtain vacuole form.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810917902.XA CN109084952B (en) | 2018-08-13 | 2018-08-13 | Potential flow theory-based calculation method for cavitation deformation of small-sized super-cavitation navigation body |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810917902.XA CN109084952B (en) | 2018-08-13 | 2018-08-13 | Potential flow theory-based calculation method for cavitation deformation of small-sized super-cavitation navigation body |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109084952A true CN109084952A (en) | 2018-12-25 |
| CN109084952B CN109084952B (en) | 2020-09-11 |
Family
ID=64834553
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810917902.XA Active CN109084952B (en) | 2018-08-13 | 2018-08-13 | Potential flow theory-based calculation method for cavitation deformation of small-sized super-cavitation navigation body |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109084952B (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112230547A (en) * | 2020-10-26 | 2021-01-15 | 哈尔滨工程大学 | Supercavitation navigation body H∞Controller design method |
| CN112380784A (en) * | 2020-09-29 | 2021-02-19 | 西北工业大学 | Super-cavity projectile without tail wing and design method thereof |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103245485A (en) * | 2013-04-16 | 2013-08-14 | 哈尔滨工程大学 | Judging device of sudden change character of ventilated supercavity balance point and judging method of sudden change character of ventilated supercavity balance point |
| KR101353410B1 (en) * | 2013-06-21 | 2014-01-21 | 엘아이지넥스원 주식회사 | Underwater moving body |
| CN105975700A (en) * | 2016-05-10 | 2016-09-28 | 北京理工大学 | Numerical method simulating ultrasonic cavity dynamics behavior |
| CN107300456A (en) * | 2017-07-06 | 2017-10-27 | 中国人民解放军国防科学技术大学 | A kind of supercavity experimental rig and test method |
| CN108388742A (en) * | 2018-03-05 | 2018-08-10 | 北京空间技术研制试验中心 | A kind of simulating analysis of spacecraft separation with pressure |
-
2018
- 2018-08-13 CN CN201810917902.XA patent/CN109084952B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103245485A (en) * | 2013-04-16 | 2013-08-14 | 哈尔滨工程大学 | Judging device of sudden change character of ventilated supercavity balance point and judging method of sudden change character of ventilated supercavity balance point |
| KR101353410B1 (en) * | 2013-06-21 | 2014-01-21 | 엘아이지넥스원 주식회사 | Underwater moving body |
| CN105975700A (en) * | 2016-05-10 | 2016-09-28 | 北京理工大学 | Numerical method simulating ultrasonic cavity dynamics behavior |
| CN107300456A (en) * | 2017-07-06 | 2017-10-27 | 中国人民解放军国防科学技术大学 | A kind of supercavity experimental rig and test method |
| CN108388742A (en) * | 2018-03-05 | 2018-08-10 | 北京空间技术研制试验中心 | A kind of simulating analysis of spacecraft separation with pressure |
Non-Patent Citations (2)
| Title |
|---|
| 张学伟等: "基于Logvinovich独立膨胀原理的超空泡形态计算方法", 《兵工学报》 * |
| 杨武刚等: "势流理论的一种数值方法在空泡形态中的应用", 《火力与指挥控制》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112380784A (en) * | 2020-09-29 | 2021-02-19 | 西北工业大学 | Super-cavity projectile without tail wing and design method thereof |
| CN112380784B (en) * | 2020-09-29 | 2024-03-19 | 西北工业大学 | Super-cavitation projectile without tail wing and design method thereof |
| CN112230547A (en) * | 2020-10-26 | 2021-01-15 | 哈尔滨工程大学 | Supercavitation navigation body H∞Controller design method |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109084952B (en) | 2020-09-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Bixler et al. | Analysis of a swimmer's hand and arm in steady flow conditions using computational fluid dynamics | |
| De Marco et al. | Experimental and numerical hydrodynamic analysis of a stepped planing hull | |
| Li et al. | Bubble-sphere interaction beneath a free surface | |
| CN106650046B (en) | A kind of unsteady characteristic acquisition methods in Ship Air flow field | |
| Silva et al. | Analysis of drafting effects in swimming using computational fluid dynamics | |
| Landrini et al. | The fluid mechanics of splashing bow waves on ships: A hybrid BEM–SPH analysis | |
| CN109084952A (en) | Calculation method based on the small-sized supercavitating vehicle vacuole deformation of potential flow theories | |
| Phan et al. | Numerical analysis of an unsteady natural cavitating flow around an axisymmetric projectile under various free-stream temperature conditions | |
| Grosenbaugh et al. | Nonlinear free-surface flow at a two-dimensional bow | |
| Lu et al. | Numerical investigation of water-entry characteristics of high-speed parallel projectiles | |
| Jin et al. | Numerical study of ventilated cavitating flows with free surface effects | |
| Van Houwelingen et al. | Effective propulsion in swimming: grasping the hydrodynamics of hand and arm movements | |
| Zhou et al. | Development of a multiphase cavitation solver and its application for ventilated cavitating flows with natural cavitation | |
| Yang et al. | Calculation of ship sinkage and trim using unstructured grids | |
| Li et al. | Fluid dynamics of biomimetic pectoral fin propulsion using immersed boundary method | |
| Donnelly et al. | Numerical simulation of flow about a surface-effect ship | |
| Scolan et al. | Water entry of a body which moves in more than six degrees of freedom | |
| Semenov et al. | Water entry of an expanding body with and without splash | |
| Shojaeefard et al. | Numerical investigation of oscillation frequency and amplitude effects on the hydrodynamic coefficients of a body with NACA0012 hydrofoil section | |
| Malazi et al. | Investigation of a longfin inshore squid's swimming characteristics and an underwater locomotion during acceleration | |
| CN114077770A (en) | Direct wave generation method for simulating water forced landing SPH (flying wave height) of aircraft | |
| Hu et al. | The structures of unsteady cavitation shedding flow around an axisymmetric body with a blunt headform | |
| CN112668256A (en) | Vertical seam type fishway vortex identification method | |
| Gan et al. | Numerical investigation of the water-entry impact performance of a bionic unmanned aerial-underwater vehicle | |
| CN111368430A (en) | Method for estimating post-ignition gas effect in water of vertical launching navigation body |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |