Virtual Modeling of tensile structure based on Frame-Grid template Текст научной статьи по специальности «Физика»

TECHNICAL SCIENCES

VIRTUAL MODELING OF TENSILE STRUCTURE BASED ON

FRAME-GRID TEMPLATE

Popov E.V.

Nizhegorodsky State Architectural and Civil Engineering University

Nizhny Novgorod, Russia Popova T.P.

National Research University Higher School of Economics

Nizhny Novgorod, Russia Rotkov S.I.

Nizhegorodsky State Architectural and Civil Engineering University

Nizhny Novgorod, Russia

ABSTRACT

The paper describes the Frame-Grid template developed to efficient form finding of the lightweight structure. The basis for the model is a special Frame object consisting of a set of spatial edges connected with each other. Mathematically it represents a graph with circuits. Generally, edges are straight lines or circle arcs. The surface of a tensile structure is represented by a stretched grid. The grid is hung on the Frame object and is subjected to optimal surface form finding by the Stretched Grid Method (SGM). The Frame edges and nodes correspond to fabric structure singularities and to boundary constrains. Topological triangles or rectangles of the Frame appear as cloth initial patches. The final structure surface inherits geometric properties from the Frame object. Therefore, the Frame-Grid template makes it possible to redefine the surface form automatically modifying only the Frame structure. The model allows taking into account the structure symmetry conditions.

Keywords: Tensile structure; Frame-Grid template; Polygon Triangulation; Stretched grid method, Force Density Method.

1. Introduction

The principle "form follows effect" is particularly relevant in lightweight tensile structures that transfer their loads purely through axial or in-plane forces. In case of the lack of bending, the external effect determines mainly the shape of the structure. The number of constrains, cables or/and hanging points usually determines the nature of such an effect. The shapes of such structures are not known in advance contrary to the conventional structures. Besides, one common problem is that lightweight tensile structures are difficult to draw and still harder for the client to visualize. Therefore, a stage of preliminary design usually precedes structure analysis in detail. The preliminary design of tension structures involves the determination of the initial configuration referred to as form finding because of the direct relationship between form and force distribution. In general, there are two ways of form finding: the physical form finding procedure and the analytical one. The physical modelling of lightweight structures has limitations for some reasons concerning labour consuming and scale problem. Therefore, the analytical form finding by computational modelling of lightweight structures is becoming more and more general. Moreover, nowadays without this technology a tensile structure cannot be built at all.

One of the widespread ways of analytical form finding is Finite Element Method (FEM). The surfaces are subdivided into a number of small finite elements such as triangles, for example. Then, all possible geometries can be calculated. However, lightweight structures possess form-active shapes. Therefore, their form

finding usually requires non-linear FEM for structures subjected to large deflections. We should mention several formulations of the FEM in large deflections used to solve the form finding problem. Among them are the techniques described by M.Barnes [1], B.Tabarokk [2], E.Moncrieff and L.Gründig [3], [4], R.Haber and J.F.Abel [5], Hewgill [6], Wagner [7], Greenspan [8]. These approaches result in the appearance of highly complex finite element stiffness matrices. Due to the nonlinearity, the number of iterations can be very high (10 - 20 or more) for each shape variant (see [9]). It results in relatively high costs for the computational analyses, which should be added to the intrinsic cost-effectiveness of this type of structures.

The force density method was developed in the early 70s in response to the need for computational structure modelling for the Munich Olympic complex [10]. The method based on the force density ratio for entire cable element produces a set of linear equations, which one can solve directly. The Force Density Method (FDM), first introduced in [11] and then developed in [12], is further often used in engineering to find the equilibrium shape of a structure consisting of a network of cables with different elasticity properties when stress is applied.

This paper describes a specially developed Frame - Grid model. This model consists of two parts, which are the Frame object and the Grid object respectively. Hierarchically, the Grid object is a descendant of the Frame object. It means that if we change the geometry of the Frame object we can obtain a new optimal form of the Grid object automatically due to a very efficient

relaxation technique based on the Stretched grid method (SGM) described in [13], [14]. In contrast to FDM SGM uses constrained stretched grid that converges to equilibrium state due to the minimum energy function. In this case, the problem is reduced to the solution of linear equations too, but this approach is much easier to implement than FDM.

2.The Frame object

Actually, the Frame object is a template for the

Figure 1. Typical Frame object

The Frame vertices usually correlate either with the points of the cloth hitch to the tent or with the points at which the cloth patches should change their geometry. The Frame edges are the subject to definition depending on two criteria, namely, the changing of fabric cloth geometry and fabric cloth boundary constrains. The fabric cloth of a tensile structure obviously needs to be attached to the supporting structure somehow. Therefore, the proper kinematic boundary condition should correspond to each edge and each vertex of the Frame object. There are two principal approaches here: a continuous fixed edge and a scalloped edge with attachment points just at the corners. The scalloped edge incorporates a fabric pocket or "cuff' through which a supporting cable is run. The assumption mentioned above results in three types of edge boundary constrains, i.e. free edge, "elastic" edge and fully constrained edge. We can list it in the following characteristics:

1. An edge that can vary its form freely like other usual grid edges. Such an edge is usually a joint between two fabric patches. Its status is "free".

2. Fully constrained edge. Such an edge and its status is "fixed".

3. The status may be "elastic" if an edge has a supporting cable-preventing warp.

Similarly, vertices can have three types of boundary conditions:

1. "free" vertex;

2. "fixed" vertex;

3. "elastic" vertex. The third type allows simulating cables to stretch fabric cloth.

Each circuit that covers, in general, non-convex, non-planar fabric membrane, can have triangular or rectangular form, the vertices of which belong to the surface. At the same time, the vertices belong to the

tensile fabric structure to be designed. It consists of a set of vertices and edges. The edges can either be straight lines or circle arcs. The Frame object is mathematically a graph with simple cycles G (V,R,A), where V - the set of vertices defined by its coordinates X, Y, Z; R - the set of edges linking the adjacent vertices, A - the set of attributes defining the edge types of either linear or curvilinear and boundary conditions. A set of cycles C (V,R) corresponds to a tensile fabric structure patches. The typical Frame object is shown in Fig. 1.

Figure 2. The Frame object with two symmetry planes

Frame object. The Frame object circuit is a part of fabric cloth to be relaxed. Actually, the circuit bounds are the Frame object edges. However, when creating an object it is critical that the current circuit is empty if there is no surface in the structure cloth.

The fabric tensile structures can very often have several symmetry planes. In this case, when developing a Frame object, one can take into account such symmetry planes. At the same time, the corresponding edges should have zero displacements in the direction orthogonal to the plane of symmetry. For example, Fig. 2 shows the Frame object that has two symmetry planes.

3.The Grid object

The second part of the Frame-Grid template is a Grid object. The Grid object is a set of triangular cells, based on topological triangles and rectangles of the Frame object. To produce the whole Frame-Grid template we should generate a triangle grid covering all the Frame object patches. This is the most critical stage of the Frame-Grid template development.

The main requirement is to produce the Grid automatically. It means that such a process should be hidden from the user. Thus, the automated generation procedure produces a triangle grid. The key concept of the procedure is to generate the triangle grid for all Frame object 2D patches successively. For this purpose, we need an appropriate and efficient 2D mesh generator. There are plenty of 2D triangle generators and the most popular is the family based on Delaunay algorithm [15]. We apply the Umansky algorithm described in works [16], [17] due to its rapidity and stability. The first step of the procedure is to split all the Frame object segments into sub segments according to the given density. This density influences the density of the final triangle. We define a Grid object in the following way:

first, we should find a segment with the minimum Cartesian length and decide how many sub segments it should be split into. Then we should split it into sub segments. The next step consists in finding the segments adjacent to the minimum one and split it into sub segments too. The scheme of splitting is based on the relation of sub segments length according to linear series. Let us assume that the minimum segment density is N. Then the length of sub segments is a = L/N where L - the length of minimal Frame object segment. In this case, the length of the first sub segment of the segment adjacent to the minimal one should be not more than 5L/N to avoid the triangles stretched too much to appear. The length of the last sub segment can be defined by a similar consideration. Finally, if the lengths of the first and the last sub segments are known then calculations aimed at the intermediate sub segments definition can be summarized by the following algorithm

M = —-, (1)

ai + aM

where M - number of sub segments; S - length of the segment; a1 - length of the first sub segment; aM - length of the last sub segment.

Further, let us assume that t is a dimensionless parameter related to the segment. This parameter can vary between 0 and 1, where 0 corresponds to the first segment vertex and the second segment vertex meets 1. Then we can calculate the co-ordinates of all intermediate nodes on the segment between the first and the second vertices by the following equation

tk =

(ak + 8k(k -1)/2)

S

k = 1.

.M(2)

8 =

(S - 2a,M )

(3)

M (M -1) '

Based on the linear series this scheme enables us to obtain intermediate nodes distribution on a segment condensed to the first or the second segment vertex depending on the relation of the first and second sub segments length.

Once the entire Frame object segments are split into sub segments, we can triangulate the entire Frame

patches. We use the triangle grid generator based on the Umansky algorithm. This algorithm permits obtaining the triangle grid that meets the Delaunay criterion. To obtain it the following requirements for the triangular cell are considered [16], [17]:

1) If nodes n1, n2 and n3 are the vertices of a triangle cell, then the vertices must be seen from the top of the triangle normal vector in the counter-clockwise direction i.e., n:^n2^n3^n: or the triangle area must be positive

ART = 1 [xi (y - y) + x (y - y) + x (y - y )]> 0, (4)

where (x1, yi), (x2, >>2), (X3, y3) are the coordinates of the nodes m, n2 and n3 respectively.

ART - the triangle area.

2) The smallest angle of the triangle must not be less than 30°. This requirement can be written in the following way

«1 *f M«= ^X« £f) (5)

3) The largest angle of the triangle must not exceed 90°:

«1 X«2 )A[«3 ) (6)

The key concept of the Umansky algorithm is a floating bound shown in Fig. 3. The concept is to fill the initial polygon by triangles. First, we should consider the initial polygon bound as the floating bound and find a node of it with the minimum angle between two adjacent lines. Next, we form one or two triangles from polygon bounds towards the polygon center according to two methods. Both methods are shown in Fig. 4. The first method of triangulation is to enclose the triple of boundary nodes as shown in Fig. 4a. We apply this method if an angle between lines (/'-1, i) and (i, i+1) is less than n/2. Otherwise, we should apply the second method (see Fig. 4b). The second method consists of two steps. The first step is to build a bisector of angle between lines (i-1, i) and (i, i+1). At the second step we locate a new node i+2 of the floating bound at the distance from node i equal to arithmetic mean of lines (i-1, i) and (i, i+1) length. Then we enclose two triangle areas to form a new floating bound.

Figure 3. The floating bound concept of the Umansky triangulation

a

Figure 4. Two ways of triangulation

The first method of triangulation reduces the number of floating boundary nodes by one unit. The second method keeps them constant. Then we form a new floating bound and repeat the process while the number of boundary nodes is not equal to 3. There can be curvilinear patches as a part of a Frame object because of possible arc lines. Another reason that can result in curvilinear patches is a non-planar location of vertices of rectangular samples. In this case, we modify the grid generator so that we can apply the same 2D procedure to a curvilinear patch triangulation. The main idea here is to substitute a curvilinear patch by its plane mapping,

triangulate it and map a grid back onto the initial patch. The general scheme of the process is shown in Fig. 5, where Fig. 6a illustrates the initial curvilinear patch. Note that we consider the curvilinear triangle shown in Fig. 5 as a curvilinear degenerate rectangle. We substitute all non-linear segments by straight lines and then split them into several sub segments as usual linear segments (see Fig. 5b). Further, we apply the usual 2D generator to create the plane mapping of the patch shown in Fig. 6c. Finally, we can map the triangle grid back onto the curvilinear patch (see Fig. 5d).

Figure 5. The triangulation of a non-linear patch using plane mapping

As an example, Fig. 6 represents a triangular ini- as generalized curvilinear octagons, we can present

tial grid based on the Frame, shown in Fig. 1 We make these functions in the following way [18]. the reverse mapping by the finite element form functions of the serendipity family. Assuming the patches

^ =-t(!-^X1 + ^ + " 1 "

4

N 2 = -1(1 + -0)(i-n + 4);

N3 =-1(1 + ?)(1 + 0)(i -v-4);

N 4 =- 1(i-i)(i + № + n-4);

N5 =-(i-^)(i-0); i

N6 = -a+i)(i-02); i

N7 = ^i-I2)(i+0); i

N5 = ^i-^)(i-02);

(7)

The number of form functions relates to the vertex

where Xi - Cartesian co-ordinate of an arbitrary

number as shown in Fig. 7. The Cartesian co-ordinates node inside of the patch at axis i,

of the final patch are calculated by the equation given below

X,j- Cartesian co-ordinates of node j = 1...8 at

x =ZXN

j=i

(8)

axis i.

Figure 7. The parametric octagon for nonlinear reverse mapping

Figure 8. The draft triangulation for non-planar rectangular patch

In the case of non-planar rectangular patch we use another approach. Three arbitrary vertices of a rectangle are chosen to calculate the characteristics of a temporary working plane. Then the entire rectangular vertices are normaly projected onto this plane to obtain a draft rectangle. We triangulate this rectangle in a standard way but we drop boundary nodes and vertices onto real rectangle segments as shown in Fig. 8.

4. Relaxation

The Frame-Grid model is a subject for relaxation by the Stretched Grid Method (SGM). This method per-

mits minimization of the surface embodied into generally non-plane closed contours. The physical meaning of SGM is the energy balance of an arbitrary grid bounded by rigid 3D contour. This provides much more plain final algebraic equation system than the usual FEM because the entire members of the final matrices are natural numbers. We do not need any integration and can calculate matrices with the help of grid topology analysis only. There is a generalised expression for SGM (see work [14])

n = X DjRJ + X (X ck (X )2 -X Pk ^xlk ),

j=i

i = 1,2,3

(9)

i=1 k=1

k=1

3

n

m

m

where n - number of grid edges, m - number of grid nnodes, Rj - length of edge number j, Dj - weight of grid edge number j, AXik - coordinate increment of node k at axis i, Cik - flexibility of an elastic constrain in node k at axis i,

Pik - outer force in node k at axis i, We can apply expression (9) to the previously generated triangle grid to relax it in the following way. Let us suppose that co-ordinate vector {X} of all nodes is associated with a final grid and the co-ordinate vector {X}' is associated with an initial grid. Thus, vector {X} will look like this

(x} = (x} + [ax}, (10)

where (AX) - vector of all nodal co-ordinate increments.

To determine vector (AX) we should derive function (9) by incrementing vector (AX) with form (10) taken into account, i.e.

du

-= 0, (11)

QAXfl

where l - the number of the network inner node,

j - the number of co-ordinate,

Let us assume that the constants in expression (9)

are Dj = D; Clk = Clk / D = 0; Plk = Plk / D = 0

and the parameter i = i,2,3 without loss of generality. Then taking into consideration expressions (10) and (11) we may obtain the following three independent systems of linear algebraic equations (see [13], [14])

[a]{ax }={bi } (12)

where [A] - symmetrical matrix in the banded form;

(AXi) - incremental vectors of nodal coordinates at axes l=i,2,3;

(Bi) -known right hand vectors. The following form may calculate the right hand vector

N

Blt = L Xlk

Xltn

(13)

k=1

Here n - total number of nodes that surround node number t,

l - the number of global axes.

Matrix [A] of the linear equation system is sparsely populated. It is a symmetrical matrix in banded form similar to the global stiffness matrix of a FEM assemblage (see for more details [9]). One can note that the usual FEM procedures for the matrix width and equation system solution are suitable here.

The surface bounded by a non-plane closed curve converges into the minimum due to the minimum of function (9). We can prove it, for instance, using the Heronian for a single triangle

Sa =VP ■ (P -ai) ■ (P -a2) ■ (p -a3),(14)

where SA - the square of one triangle,

P_

p= ~ - semi-perimeter of the triangle,

ai - the length of side i.

Let us transform exp (14) further into

5.=1 A 4'

where

a2 = x ji+1 + Ax ji+l) ■ j=1

xji+i,xji - co-ordinates j of the 2nd and the 1st nodes of triangle edge i,

Ax ji+1, Ax ji - decrements of nodal co-ordinates respectively.

Function (15) is non-linear with respect to nodal

vector Ax j . However, we can immediately notice that for function L the following non-equality

3

(x ji + A

ji

)}

2

3 3

(Y^a2)2 - ¿La4 i i

i = 1,2,3; j=1,2,3

(15)

where nx is the first component of function (9)

that

is nx =^[JD]R2 with

D, = 1 and

j=i

L =1L2 > 5a = 1

3 3

(La2)2 -2La4

1

1

(16)

is always true at any nodal vector Ax j . Hence,

we

may affirm that if vector Ax j minimizes function L

then it also gives the minimum to function Sa .

If we write, further the total 3D surface area with a triangular grid as a sum of areas of all triangles

n

S1= C I S A , (17)

k =1

we may also notice here that the following expression is always true

u > , (18)

Rj =■>!(X 12 -X1l) 2 + (X22 -X2l) 2 +(X32 -X3l) 2 ■

Thus, as it is shown above the minimum surface problem that consists of minimization of function (17) may be substituted for the minimum problem solution of function (9). This corresponds to THEOREM 1 in work [12] that is the basic proof of FDM applicability to a surface area minimization. This theorem is formulated in the following way: "Each equilibrium state of an unloaded network structure with force densities qt is identical with the net, whose sum of squared way lengths weighted by q is minimal". It means that FDM is actually a consequence of the SGM. Besides, the main advantage of SGM is that the method of obtaining the final equation system is much easier to implement than FDM and one can apply standard FEM procedures here.

As systems (12) are linear, the procedure elapses very quickly to a one-step solution. Moreover, each final interior node position meets the requirement of coordinate arithmetic mean of nodes surrounding it and meets the Delaunay criterion too. The final grid obtained after the solution of Eqs. (12) is an approximated facet structure whose area converges to the area of a related minimum surface according to the initial grid

1

refinement. The procedure is equivalent to obtaining a minimum surface subjected to the constraint of a bounded rigid framework. The example below is to demonstrate the technique for minimum surface form finding. It concerns the problem of a catenoidal surface between two concentric rings as described in [13]. The solution of this problem uses three steps. At the first

step, the initial Frame object in the form of the lateral cylinder structure is designed. Then the Frame patches are covered by a triangular mesh. The next step is concerned with the dropping of interior nodes onto the catenoidal surface. The total catenoid area (see Figure 9) is calculated as the sum of the areas of all triangles after solving Eqs. (13) to result in 2.9956 (exact 2.992).

Figure 9. The cathenoidal surface

Figure 10. The entire soap film like Frame-Grid model

Figure 11. The entire non-minimum Frame-Grid model

After relaxation, we can obtain the final Grid object that is shown in Figs. 10, 11. The first Frame-Grid template has a surface designed as a classical minimum surface (see Fig 10). The second Frame-Grid template is designed using a special adaptation algorithm to make the Grid object other than the minimum surface. As it is noted by some researchers (see for example [2], [7]), the minimum surfaces do not always meet the requirements of customers because of the inefficient use of structure storage space. In this case we apply nonlinear function for each weight ratio of Grid edge separately. This algorithm uses Dj - weight ratio of each grid structure edge mentioned in form (9). This ratio does not count in the solution when finding the minimum surface form. Therefore, we can consider it equal to 1 for the entire Grid object edges with the loss of generality. Otherwise, we may express the function for weight ratio in the following form

D, = D . xe

J 0 J

where Doj - initial weight of the edge number j;

Lj and Loj - the length of the edge number j at the iteration and its initial length respectively.

We apply form (18) to current edge only when the power of the exponent is positive. It happens when the current edge is stretched during the solution. The solution is done iteratively. In our sample, this allows obtaining a useful storage space of the structure in about 11% more than in the minimum surface case.

The Grid object can be represented by three interrelated structures, each of which contains information about the topology and geometry of vertices, edges, and grid. The sample of these three structures is presented in Table 1, where n - number of entire vertices of the grid, k- number of edges and m - number of grid faces. From a formal point of view, such representation corresponds to the classical boundary representation (B-Rep, see. [19] - [21]).

Obviously, the Grid object is a descendant of the Frame object and inherits the entire geometric properties from it. The Vertex Table provides such inheritance. To modify the final form of the Grid object it is enough to change the Cartesian co-ordinates of the Frame object vertex/vertices only. It is supposed to be user-friendly for tensile structure designing.

Table 1.

The mathematic representation of the Grid model

m j

(18)

Face Table Edge Table Vertex Table

Face: Edges Edge: Vertices Vertex: Coord.

Fi:Ei, E5, En Ei:Vi, V2 V\:x\, y1, Z1

F2.'E3, Et, E8 E2:V2, V3 V2:X2, y2, Z2

Fm:Ek-i, Ek-2, Ek-7 Ek:Vn-1, Vn

b

Figure 12. The Frame object vertex modification to the hypar form control

a

For example, Fig. 12 illustrates the easiness with which we can modify the form of the hypar tent. Figs. 12a shows the form of the Frame object. To modify the tent as presented in Figs 12b, 12c we should only change the co-ordinates of the Frame vertex.

5.Conclusion

This paper presents a realistic modelling capability for the tensile structure form finding, which can form the principal component of an integrated design procedure for such structures. We can perfectly enable this fast and computationally efficient Frame-Grid template for general CAD-like application for surface modelling and lightweight structures design. The model has an ability to define the form of a tensile structure very

easily and quickly in one-step solution. We can consider that the developed Frame-Grid template gives high levels of flexibility in the design of tensile structure. Numerous case studies have been undertaken, which provide an enhanced understanding how we can develop the sophisticated tool for tensile structure form editing. The primary benefit brought by the developed Frame-Grid template capability appears to be more rapid control for lightweight structures design and more structure variants for the user to consider. This leads to the guarantee of higher quality structures with neater and cleaner details. It could also provide the necessary functionality for the design of ambitious tensile structures.

Figure 13. Some samples of tensile structures

In Fig. 13, one can see some examples of structures virtually designed with Frame-Grid template and further built in southern regions of the Russian Federation (with the permission of "Kubantent Co" www.kubantent.ru)

We acknowledge the support by RFBR (Russian Foundation for Basic Research) under Grant # 15-0701962 and Grant # 15-07-05110.

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ИССЛЕДОВАНИЕ ФИЗИКО-ХИМИЧЕСКИХ СВОЙСТВ СМЕСЕЙ ГАЗОВОГО КОНДЕНСАТА С ТЯЖЕЛЫМИ ТОПЛИВАМИ

Бабаев Г.М.

Азербайджанская Государственная Морская Академия, доцент

Баку

RESEARCH WORK OF PHYSICS-CHEMICAL GAS MIXTURE CONDENSATE WITH HEAVY FUEL

Babayev H.M.

Azerbaijan State Marine Academy, assistant professor

Baku

АННОТАЦИЯ

В статье проведен сравнительный анализ основных физико-химическим свойств топлив, изготовленных на основе газового конденсата.

ABSTRACT

In this article, it deals with analysis of major physics-chemical constituent of fuel, based on gas condensate.

Ключевые слова: судовой дизель, Морской Регистр, температура вспышки, дизельное топливо, печной мазут, моторное топливо, газовый конденсат, тяжелое топливо, температура кипения.

Keywords: marine engine, Marine Register, temperature of flash point, diesel fuel (oil), heavy oil, motor fuel, gas condensate heavy fuel, boiling temperature (degree).

Увеличение морских перевозок и ужесточение международных требований к экологичности современных судовых двигателей ставит перед судостроителями и судомеханиками задачи разработки новых видов топлив. В этой связи представляет несомненный интерес использование топлив подготовленных на основе газовых конденсатов [4].

Как известно, на основании требований Морского Регистра на судах могут применяться топлива с температурой вспышки в основном не ниже 610С [2]. Но поскольку температура вспышки газовых конденсатов колеблется в пределах 5^15°С, в зависимости от их месторождений, использование их в качестве топлива для судовых двигателей с точки зрения безопасности не разрешается.

Для проведения исследований нами был использован газовый конденсат из месторождения «Булл-море» в Азербайджанском секторе Каспийского моря.

Используемое в судовых двигателях тяжелое топливо в 2^2,5 раза дешевле, чем дизельное топливо. Но более низкое качество, по сравнению с дизельным топливом и необходимость его дополнительного подогрева и очистки увеличивает общую себестоимость топлива, уменьшает экономичность и моторесурс двигателя. Начиная с 2003 года на кафедре «Судовые энергетические установки» Азербайджанской Государственной Морской Академии

проводятся научно-исследовательские работы в целях исследования способов повышения температуры вспышки топлив на основе газовых конденсатов. Для решения поставленных задач нами в качестве двигателя был взят вспомогательный судовой дизель марки 2Ч 10,5/13.

Исходя из сказанного, в первую очередь, были исследованы возможности изменения температуры вспышки смеси тяжелого топлива с газовым конденсатом с высокой температурой (свыше 100°С) вспышки. Но было установлено, что при уменьшении количества газового конденсата в смеси до 10% температура вспышки топлива не поднимается выше 20^30°С, что не является приемлемым результатом.

Далее были проведены исследования по изменению температуры вспышки после повышения подогрева газового конденсата 80°С до 120°С, с целью удаления сравнительно легких фракций. Изменение температуры вспышки в зависимости от температуры подогрева, которую условно назвали температурой кипения, показана на рисунке 1.

Как видно из рисунка 1, по мере повышения температуры подогрева газового конденсата его температура вспышки возрастает прямолинейно. Если после подогрева газового конденсата до 80°С его температура вспышки достигает 25°С, то при подогреве до 100°С и 120°С повышается до 31°С и