Abstract

Experimental and numerical investigations on the protection efficiency of a diamond-shaped thermal jacket made of the certain braided composites with anisotropic material properties for gun barrels were carried out to gain an insight into its thermal–structural behavior and performance. The experiments for the gun barrels with and without the thermal jacket subjected to unilateral thermal radiation were conducted on a thermal jacket protection efficiency experimental system. Three-dimensional finite element models were established to perform the thermal–structural analysis and approximate the temperature distribution and thermal deformation of the shrouded gun barrel and bare gun tube. The experimental results validated the numerical models for the study of solar radiation on the thermal–structural characteristics of the gun barrels with and without the thermal jacket. The temperature changes together with their gradients, and the thermal deformation of the gun tube shrouded with the thermal jacket were notably less than that of the bare gun tube. The nonuniform temperature distribution caused by unilateral radiation can be substantially ameliorated by the thermal jacket. The developed diamond-shaped thermal jacket owned satisfactory protection effectiveness. In addition, moderately increasing the thermal jacket's thickness or the air gap between the thermal jacket and gun tube can decrease the muzzle deflection of the shrouded gun barrels. The work is promising in providing both theoretical and practical contributions in design of shrouded tank gun barrels aiming at achieving high first shot accuracy.

Introduction

When a tank gun is exposed to solar radiation, wind or rain, uneven heating or cooling at different sides of the gun barrel happens, causing cross section temperature gradient of the gun barrel. The induced thermal deformation of the gun barrel affects the impact point and consequently degrades the shooting accuracy of the tank system [1]. To reduce the bending deformation of the gun barrel intrinsically resulting from the thermal distortion, and improve the first shot accuracy of a tank system, a thermal jacket consisted of a set of sleeves or covers is widely shrouded on the gun barrel [2]. A thermal jacket decreases the temperature gradients of the gun barrel that lead to the thermal distortion. Thermal jackets can be typically divided into three types according to their different structural styles and working principles, including the heat insulation, heat conduction, and complex types [3]. A thermal jacket of the heat insulation type impedes heat exchange between the barrel and the outside, and reduces the influence of external heating or cooling on the barrel, due to the effects of thermal insulation materials. It provides a convenient way to suppress the thermal distortion of a gun barrel, as different material properties and physical form of thermal jackets have different heat insulation capacities. In order to systematically and quantitatively ensure the protection performance, the efficiency of a thermal jacket needs to be tested and evaluated after it is processed.

In the past, some researchers have analyzed the thermal distortion of gun barrels and protection effectiveness of thermal jackets through experimental and analytical approaches. Minor et al. [4] developed an analytical heat transfer model to describe the temperature distribution in a multilayer, shrouded gun tube, and obtained the performance by solving the two-dimensional thermal equation for each of concentric cylinders which simplified from the gun, air gap, and five jacket layers. In that model, the material properties of the cylindrical layers of the glass fiber reinforced composite jacket were assumed to be isotropic. To investigate the deformation of a gun tube resulting from the initial imperfections, Kingsbury and Kalbag [5] worked out an exact solution for the gun muzzle displacement by formulating an expression for the complementary strain energy of deformation of the idealized beam. Cote [6] theoretically studied the gun muzzle orientation attributed to thermal stress of the tube with thermal shrouds generated by temperature differences. A simulated solar heating apparatus, in which the array of heat lamps was arranged and lengthened to give the desired heat flux to the gun barrel, was constructed to measure the performance of various thermal jackets on a gun tube. Bundy and Patton [79] proposed experimental methods to simulate the thermal effects of gun firing, used various laboratory heating devices to deliver heat to the barrels, and accordingly explored the variation in shot impacts due to controlled bending of a gun. Liu and Pan [10,11] conducted the research on protection efficiency test for the thermal jacket of gun barrels, and utilized the proposed parameter adjustment method to correct the thermal radiation deviation induced by the environmental disturbances. Birulya [12] developed a stand equipment to simulate weather factors as solar radiation, rain and wind, carried out a series of tests to evaluate the effectiveness of heat-shielding housings for a tank gun made of composite materials. Numerical simulations based on finite element methods have been developed and widely employed to analyze heat transfer and thermal distortion problems, in respect that they are extraordinarily practical for industrial applications. By utilizing the finite element methods, many researchers have investigated the heat transfer problems for bare single layer or multilayer barrels [1316], and some other researchers carried out numerical simulations of thermal characteristics in tubes of heat transfer equipment [1719]. Further, Han [1] analyzed the effectiveness of thermal shroud on the thermal deformation of a gun barrel by the finite element method. Ahn [20] developed a numerical model for evaluating the thermal shroud effect on the performance of a gun barrel, and carried out experiments to validate the model. Bogomolov et al. [21] performed a numerical and experimental investigation of solar radiation on the gun barrel with a heat-protective housing, to assess the effectiveness of the thermo-protective covers made of polymer composite-fiber materials.

Shape stealth technology is more and more widely used in design of tanks. Most of the thermal jackets in application are cylindrical structures, without stealth performance. In order to make tanks difficult to be detected by known radar observation methods, a diamond-shaped thermal jacket can be used. Nonetheless, reports are scarce in the literature regarding the investigation of diamond-shaped thermal jackets, where the heterogeneous structure play an important role in the effect of the thermal process. With regards to material constitutive relations, the existing studies usually focus on isotropic thermal-elastic models. The main motivation of this work is to perform an experimental and numerical study to evaluate the protection efficiency of a diamond-shaped thermal jacket made of braided composites, in order to better understand the effects of the geometric configuration and anisotropic material properties on the performance of the thermal jackets.

Experimental Investigations.

This section describes the experimental investigations carried out to obtain the protection performance of a diamond-shaped thermal jacket. The gun tube was made of gun steel. The hybrid carbon-fiber/glass-fiber reinforced epoxy resin composites were braided into the desired shapes for the thermal jacket. The schematic representation of the gun barrel shrouded by the diamond-shaped thermal jacket is shown in Fig. 1. The geometry and structural parameters of the shrouded barrel are listed as follows: the caliber of the gun tube was 105 mm. The barrel length was L, the length of the diamond-shaped thermal jacket section I was L1, the length of section II was L2, and the length of section III was L3. A small flat surface was designed on section I to make way for the line of sight, because the front end of the barrel needed to be equipped with an aimer. The width of the thin end of the diamond-shaped thermal jacket was W1, the height of the thin end was H1. The width of the thick end of the thermal jacket section I was W2, and the height was H2. The width of the rear end of the thermal jacket was W3, and height of the back end was H3. The units of the lengths are in millimeters. The thickness of the thermal jacket was 2 mm. The jacket thickness was typically measured at several key points along the length of the gun barrel to ensure uniformity and meet design specifications. These included near the muzzle (Section A), in the middle section (Sections B and C), and near the breech end (Section D), as shown in Fig. 1. The front section support IV, middle section support V, and rear section support VI were installed in the annular grooves of the barrel. The thermal jacket sections I and II were sleeved in the grooves on the clamping support mounted on the barrel. The thermal jacket section III was connected with the gun breech.

Fig. 1
Schematic representation of gun barrel shrouded by the diamond-shaped thermal jacket
Fig. 1
Schematic representation of gun barrel shrouded by the diamond-shaped thermal jacket
Close modal

The structural parameter named “air gap” seems to be a promising factor affecting the protection efficiency of thermal jackets. It is relatively convenient to define the air gap for a gun barrel with thermal jackets in a concentric circular layout. The distance between the two circles may be a clear definition. But for the current configuration, a more trivial description is needed, as the distance between a diamond shape and a circle is not easy to define, and furthermore, there is a gradient in the cross-sectional dimensions of the structure along the axial direction. For the sake of concise analysis, the dimensions La and Lb are used to measure the air gap, as illustrated in Fig. 1, and the size of the air gap is denoted by (La, Lb). The value of the air gap between the thermal jacket and gun tube during the experimental investigation was (55, 25) (units: mm, mm). In the subsequent study of parameter influences, the cross-sectional dimensions of thermal jackets are scaled as a whole for the similar reasons. Hence, it is not as convenient to describe using the dimensions rather than the scale factor. For this reason, the cross size scale factor of the thermal jacket is introduced to represent the change of air gap between the thermal jacket and gun tube.

The experiments were conducted on a thermal jacket protection efficiency experimental system. The experimental setup is shown in Fig. 2(a). It was consisted of a thermal radiation machine, a support frame, a displacement transducer, ten electric-thermocouple thermometers, a data acquisition system and a computer, as well as the gun barrel with or without the thermal jacket. The thermal radiation machine, which was mainly composed of a dimming device, an infrared light source, and a lamp frame, was used to simulate the solar exposure conditions. The strength of thermal radiation was measured by a bolometer. The support frame was used to support and fix the barrel. The back end of the barrel was attached to the support frame with the help of clamps in order to be in cantilever state, similarly as being mounted on a tank system. Muzzle deflection values were obtained by the displacement transducer. Ten electric thermocouple test points were arranged at the upper and lower surfaces of the gun tube as shown in Fig. 2(b), as well as a data acquisition system was installed, to measure temperature distribution of the gun tube and obtain the running data of the system. The obtained temperature signal was converted into the thermoelectric emf signal, and was transmitted to the computer via an analog-digital converter.

Fig. 2
Experimental setup: (a) thermal jacket protection efficiency experimental system and (b) electric thermocouple test points
Fig. 2
Experimental setup: (a) thermal jacket protection efficiency experimental system and (b) electric thermocouple test points
Close modal
The protection effectiveness of a thermal jacket for gun barrels is determined by the following formula [12]:
η=(ab)/a×100%
(1)

where η is the protection effectiveness of a thermal jacket for gun barrels, a is the vertical movement of gun muzzle without a thermal jacket, and b is the vertical movement of gun muzzle with a thermal jacket.

The experiments were conducted at the strength of thermal radiation 0.95 kW/m2 for the gun barrels with and without the thermal jacket. The obtained tube temperature and muzzle deflection of the gun barrels subjected to radiation for one hour are given in Table 1 and Fig. 3. Under the action of radiant heat, there was a temperature difference between the upper and lower surfaces of the gun tube. In general, the temperature difference of the gun tube shrouded with the thermal jacket was remarkably smaller than that of the bare gun tube at the same measuring points. As a result of the influences of the uneven temperature, the gun tubes underwent bending deformation, and the vertical displacement curves of gun muzzle were measured as shown. The obtained muzzle deflection values for the gun barrels with and without thermal jacket, as well as the measured protection effectiveness of the diamond-shaped thermal jacket for the gun barrel, were given in Table 2.

Fig. 3
Numerical and experimental vertical displacement of gun muzzle
Fig. 3
Numerical and experimental vertical displacement of gun muzzle
Close modal
Table 1

Numerical and tested temperature results

(a) Results with thermal jacket
Test point1#2#3#4#5#6#7#8#9#10#
Tested temperature (°C)Initial31.630.331.431.331.831.330.731.230.430.4
Final40.335.337.933.741.734.936.032.733.631.2
Difference8.75.06.52.49.93.65.31.53.20.8
Numerical temperature (°C)Initial31.0
Final38.536.338.336.437.035.434.833.334.032.7
Difference7.55.37.35.46.04.43.82.33.01.7
(a) Results with thermal jacket
Test point1#2#3#4#5#6#7#8#9#10#
Tested temperature (°C)Initial31.630.331.431.331.831.330.731.230.430.4
Final40.335.337.933.741.734.936.032.733.631.2
Difference8.75.06.52.49.93.65.31.53.20.8
Numerical temperature (°C)Initial31.0
Final38.536.338.336.437.035.434.833.334.032.7
Difference7.55.37.35.46.04.43.82.33.01.7
(b) Results without thermal jacket (bare gun tube)
Test point1#2#3#4#5#6#7#8#9#10#
Tested temperature (°C)Initial30.228.830.629.631.230.130.529.730.028.8
Final44.436.942.435.440.134.441.934.037.131.7
Difference14.28.111.85.88.94.311.44.37.12.9
Numerical temperature (°C)Initial30.0
Final43.438.241.737.239.735.736.833.335.131.8
Difference13.48.211.77.29.75.76.83.35.11.8
(b) Results without thermal jacket (bare gun tube)
Test point1#2#3#4#5#6#7#8#9#10#
Tested temperature (°C)Initial30.228.830.629.631.230.130.529.730.028.8
Final44.436.942.435.440.134.441.934.037.131.7
Difference14.28.111.85.88.94.311.44.37.12.9
Numerical temperature (°C)Initial30.0
Final43.438.241.737.239.735.736.833.335.131.8
Difference13.48.211.77.29.75.76.83.35.11.8
Table 2

Numerical and tested protection effectiveness of the diamond-shaped thermal jacket

Muzzle vertical movement with thermal jacket (mm)Muzzle vertical movement without thermal jacket (mm)Protection effectiveness (%)
Tested0.582.04571.6%
Numerical0.682.8776.3%
Muzzle vertical movement with thermal jacket (mm)Muzzle vertical movement without thermal jacket (mm)Protection effectiveness (%)
Tested0.582.04571.6%
Numerical0.682.8776.3%

Numerical Simulations of the Thermal–Structural Actions.

Three-dimensional thermal–structural analysis by finite element methods can be conducted to approximate the transient temperature and geometrical distortion of a shrouded gun barrel and bare gun tube. The numerical results will be evaluated by comparing with the experimental data. Considering the details according to the previous described situations, heat transfer in the gun barrels exposed to the thermal radiation, as well as the thermal deformation characteristics, should be analyzed first.

Thermal Model.

The main geometry of the gun barrel shrouded with the diamond-shaped thermal jacket is designed as illustrated in Fig. 4. The diamond shroud represents the thermal jacket made of the certain composite material, and the hollow cylinder in the center represents the gun tube. As axial temperature gradients are considerable compared to transverse gradients, and a heating environment is of highly regarded, a three-dimensional transient heat transfer model is considered. The model can be described by the following equation [22,23]
x(kxTx)+y(kyTY)+z(kzTz)+Φ˙=ρcTt
(2)

where T is the temperature; t is the time; ρ is the density; c is the specific heat capacity; kx, ky, kz are the thermal conductivity in different directions; x, y, z are the axis directions in a rectangular coordinate system, respectively; Φ˙ is the generated heat energy per unit volume. Here, no internal heat source is considered, then Φ˙=0.

Fig. 4
Thermal model and boundary conditions
Fig. 4
Thermal model and boundary conditions
Close modal

The surface convection and radiation of the exterior surface of the thermal jacket, as well as the convective effects of the inner surface of the gun barrel are taken into account. The effects of the surface radiation in the bore of the gun barrel are negligible. The boundary conditions (shown in Fig. 4) of the thermal problem are nonlinear, and can be described as follows.

The boundary condition for the upper surface A of the thermal jacket is written as
qA=nGiαhA(TAT)εAσ(TA4T4)
(3)
The boundary condition for the lower surface B of the thermal jacket is written as
qB=hB(TBT)εBσ(TB4T4)
(4)
The boundary condition for the inner surface E of the gun tube is written as
qE=hE(TET)
(5)

where qA, qB, qE are the heat flux of the upper surface A, lower surface B, and surface E, respectively; Gi is the solar flux; n is the normal vector of the upper surface A; α is the absorbency of the thermal jacket; hA, hB, hE are the convection coefficient between the upper surface A, lower surface B, surface E, and surrounding atmosphere, respectively; εA, εB are the emissivity of the upper surface A and lower surface B, respectively; TA, TB, TE are the surface temperature of the upper surface A, lower surface B, and surface E, respectively; T is the ambient temperature; σ is the Stefan–Boltzmann constant (5.67 × 10−8 W/m2 K4).

The heat transfer due to the radiation across the air gap between the thermal jacket and gun tube can be calculated by the Stefan–Boltzmann equation [24]
qCD=εσACFCD(TC4TD4)
(6)

where qCD is the heat flux; ε is the emissivity, which is determined by the emissivity of two objects, εC and εD; AC is the area of inner surface C of the thermal jacket; FCD is the radiation angle factor (also known as shape factor) between the two surfaces; TC is the absolute temperature of surface C; and TD is the absolute temperature of the outer surface D of the gun tube.

Thermal Stress Formula.

As the temperature increase ΔT (x, y, z) in elastic solids is known, the thermal-elastic constitutive relation is as follow:
σij=Dijkl(εklεij0)
(7)
where σij is the stress tensor; Dijkl is the elastic modulus tensor; εkl is the strain tensor; εij0 can be expressed by
εij0=[αxxΔTαyyΔTαzzΔT000]T
(8)
For general elastic solids, the detailed expression of each term is referred to Ref. [25]. For an orthotropic composite material concerned, the elastic modulus tensor in the constitutive equation of thermoelasticity can be expressed as [26]
Djkl1i=[1ExμyxEyμzxEz000μxyEx1EyμzyEz000μxzExμyzEy1Ez00000012Gyz00000012Gzx00000012Gxy]
(9)
where
μyzEy=μzyEz,μzxEz=μxzEx,μxyEx=μyxEy

The nine elastic constants in the orthotropic constitutive equation are comprised of three Young's modulii Ex, Ey, Ez, the three Poisson's ratios μyz, μzx, μxy, and the three shear modulii Gyz, Gzx, Gxy.

Except the physical equations mentioned above, the equilibrium equation, boundary conditions, and geometric equations are almost the same as those of ordinary elastic problems. The general expression of the principle of virtual work of the current thermoelastic problem ignoring the inertia term is
ΩDijklεklδεijdΩ(Ωb¯iδujdΩ+Spp¯iδuidA+ΩDijklεij0δεijdΩ)=0
(10)

where b¯i is the body fore in domain Ω; p¯i is the given surface force on the boundary Sp.

Let the node displacement vector of the system be q, the shape function matrix be N, the strain-displacement matrix be B. The element stiffness matrix Ke, the element force vector Pe, and the element temperature equivalent load vector P0e, respectively, can be calculated by
Ke=ΩBTDBdΩ
(11)
Pe=ΩNTb¯dΩ+SpNTp¯dA
(12)
P0e=ΩBTDε0dΩ
(13)
The finite element formula for the system can be expressed as
Kq=P+P0
(14)
in which
K=Ke,P=Pe,P0=P0e
(15)

where K is the stiffness matrix, P is the force vector, and P0 is the temperature equivalent load vector of the system, respectively. Compared with general elasticity problems, the temperature equivalent load is added into the load terms of the finite element equation.

Sequentially Coupled Thermal–Structural Analysis.

Normally, to calculate thermal stress, either a sequentially coupled thermal–structural analysis or a fully coupled thermal–structural analysis is used [27]. In the current problem, the additional mechanical loads or constraints was in conjunction with the thermal loads, nevertheless the temperature field was less affected by the stress or deformation. Consequently, a sequentially coupled thermal–structural analysis was performed in this study, the thermal analysis was conducted first and then the structural analysis was conducted by utilizing the temperature field and temperature history predicted in the previous step.

The model presented was implemented in the commercial abaqus software. The finite element mesh used in the thermal–structural analysis is shown in Fig. 5, in which Fig. 5(a) is for the gun barrel with the thermal jacket and Fig. 5(b) is for the bare gun tube. The computational domain was mainly consisted of about 3300 four-node quadrilateral elements for the thermal jacket and 19,100 eight-node linear solid elements for the gun tube. The solid elements for the section support were treated to be connected with the thermal jacket and gun tube elements in a common node mode. It seems that an appropriate balance between adequate precision of results and time consuming can be achieved by the adopted model simplification, mesh sizes, and shapes.

Fig. 5
Finite element mesh used in the analysis: (a) gun barrel with thermal jacket and (b) bare gun tube
Fig. 5
Finite element mesh used in the analysis: (a) gun barrel with thermal jacket and (b) bare gun tube
Close modal

The thermal jacket was made of braided composites, and the gun tube was made of steel. It is obvious that material behavior plays a crucial role in a thermal–structural problem. The gun tube was assumed to have the typical geometrical, mechanical, and thermal properties. The isotropic linear thermoelastic material model was adopted for the gun tube. The orthotropic elastic properties of the braided composites for the thermal jacket were considered in the analysis. Any temperature dependence of the mechanical and thermal properties was considered to be neglected. The models were shown to be able to capture the responses in the temperature distribution and thermal distortion of the gun barrels. In the current simulations, the material parameters are listed in Table 3. The material properties listed in Table 3 were provided by the manufacturer or obtained from established materials databases and scientific literature. For instance, the date of the steel for the gun tube, used in the current analysis, were taken from established materials databases and scientific literature including Refs. [1] and [28]. As to the braided composites for the thermal jacket, the data were primarily determined by the technical reports from the manufacturer. Considering the orthogonal anisotropy of the braided composites for the thermal jacket, the material coordinate system was established in the models, and the material coefficients in different directions were set. The heat transfer properties for the simulations are given in Table 4. The convection coefficients were approximately determined based on empirical correlations derived from relevant fluid dynamics and heat transfer literature (Refs. [15], [20], [21], and [29]), given the specific boundary conditions and physical properties of our system. The emissivity data of the materials used were taken from comprehensive material property databases and relevant literature (Ref. [21]). Emissivity values are intrinsic properties of materials and are typically measured experimentally under controlled conditions. However, conducting specific tests for every technical parameter of the used materials is costly and impractical. As such, when the margin of error was acceptable, we relied on previously published data for the analysis.

Table 3

Material properties for the simulations

Material parameter (unit)Braided composites for thermal jacketSteel for gun tube
Density, ρ (kg/m3)16507850
Young's modulus, Ex, Ey, Ez (GPa)230, 230, 15207
Poisson's ratio, μxy, μxz, μyz0.293, 0.202, 0.2020.3
Shear modulus, Gxy, Gxz, Gyz (GPa)5.03, 24, 24
Thermal conductivity, kxx, kyy, kzz (W/(m K))6.582, 6.582, 0.3338.1
Coefficient of thermal expansion, αxx, αyy, αzz (K−1)−1.09 × 10−6, −1.09 × 10−6, 2.43 × 10−51.23 × 10−5
Specific heat capacity, c (J/(kg K))1120460
Material parameter (unit)Braided composites for thermal jacketSteel for gun tube
Density, ρ (kg/m3)16507850
Young's modulus, Ex, Ey, Ez (GPa)230, 230, 15207
Poisson's ratio, μxy, μxz, μyz0.293, 0.202, 0.2020.3
Shear modulus, Gxy, Gxz, Gyz (GPa)5.03, 24, 24
Thermal conductivity, kxx, kyy, kzz (W/(m K))6.582, 6.582, 0.3338.1
Coefficient of thermal expansion, αxx, αyy, αzz (K−1)−1.09 × 10−6, −1.09 × 10−6, 2.43 × 10−51.23 × 10−5
Specific heat capacity, c (J/(kg K))1120460
Table 4

Heat transfer properties for the simulations

Heat transfer property (unit)Value
Convection coefficient between the upper surface A, lower surface B, and surrounding atmosphere hA, hB (W/(m2 K))5.7
Convection coefficient between the surface E and surrounding atmosphere hE (W/(m2 K))3.5
Emissivity of the upper surface A, lower surface B εA, εB0.491
Emissivity of the inner surface C εC0.9
Emissivity of the outer surface D εD0.782
Ambient temperature (° C)31.0 (30.0)
Heat transfer property (unit)Value
Convection coefficient between the upper surface A, lower surface B, and surrounding atmosphere hA, hB (W/(m2 K))5.7
Convection coefficient between the surface E and surrounding atmosphere hE (W/(m2 K))3.5
Emissivity of the upper surface A, lower surface B εA, εB0.491
Emissivity of the inner surface C εC0.9
Emissivity of the outer surface D εD0.782
Ambient temperature (° C)31.0 (30.0)

Numerical Results and Validations.

When constructing the finite element models and conducting the numerical simulations, the experimental conditions were followed as closely as possible. There was a little difference between the set initial temperature values of the numerical models for the gun barrels with and without the thermal jacket, as they were taken from the average tested temperature, respectively. Accordingly, the consistent ambient temperature values were set for the models, respectively. In terms of structure, the back end of the gun barrels was fixed. The finite element simulations were carried out using the above parameters and the radiation intensity used to predict the temperature field and deformation of the gun barrels with and without the diamond-shaped thermal jacket.

Table 1 (a) and (b) show the comparisons between the experimental and simulated temperature results for the ten electric thermocouple test points. The numerical results have a good agreement with the experimental data. It indicates that the proposed model covered the temperature field distribution and the trends of the temperature changes, so it is appropriate to apply the established model to the prediction. The cross section temperature contours of the gun barrels are shown in Figs. 6(a) and 6(b). It is noted that the numerical result of a cross section at a distance of 400 mm from the gun muzzle was chosen. The longitudinal wall temperature contours of the gun barrels are shown in Figs. 7(a) and 7(b). The shape of each cross section of the gun barrel with or without the thermal jacket perpendicular to the axial direction was basically similar, but the size changed from back to front along the axis. That is to, say, the gun tube was not a straight cylinder, and the thermal jacket was not in the shape of a straight prism. So, even if the gun barrel were heated uniformly from an external source, these internal factors arising from the structural contours and dimensions would cause the temperature to be higher at the muzzle end and lower at the breech end. The temperature changes together with their gradients of the gun tube shrouded with the thermal jacket were demonstrated to be notably less than that of the bare gun tube. The uneven temperature distribution arising from unilateral radiation can be substantially ameliorated by the thermal jacket.

Fig. 6
Cross section temperature contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Fig. 6
Cross section temperature contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Close modal
Fig. 7
Longitudinal wall temperature contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Fig. 7
Longitudinal wall temperature contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Close modal

The thermal deformation contours of the gun barrels with and without the thermal jacket are shown in Figs. 8(a) and 8(b), respectively. To give an intuitionistic and clear view of the thermal deformation of the gun barrels, the display is magnified by 100 times. The thermal deformation of the gun tube shrouded with the thermal jacket was greatly less than that of the bare gun tube. Figure 3 shows the numerical and experimental vertical displacement of the gun muzzle for different cases. The deformation behavior of the gun barrels was captured by the finite element models. For the case of the gun barrel with the thermal jacket, the numerical vertical displacement of gun muzzle was observed to be in good agreement with the experimental result. A convex upward trend at the initial stage was detected in the numerical result, probably due to the complexity of thermal–structural coupling interaction in which the anisotropy material properties of the thermal jacket were included. The particular did not appear in the test data, perhaps owing to the accuracy of the experimental system. Nonetheless, the limitations of the numerical model are not excluded. For the bare gun tube case, there were slight differences between the simulated vertical displacement of gun muzzle and the test situation. The exhibited discrepancy in prediction may be resulted from the simplified assumptions used in the simulation. Specifically, the heat transfer parameters have been treated as constants in the model, which is often done for simplicity. However, in real-world situations, these parameters can vary significantly due to factors such as changing ambient conditions, material properties, and operational statuses. For instance, differences in environmental temperature, barrel heating due to repeated irradiation, or changes in airflow around the gun barrel can all affect heat transfer and thus impact the gun barrel's performance. If these variations were not taken into account in the simulation, it could lead to relatively large deviations from the observed results. In future work, a more detailed and dynamic representation of these parameters could be integrated into the model to improve its predictive accuracy.

Fig. 8
Thermal deformation contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Fig. 8
Thermal deformation contours of gun barrels: (a) with thermal jacket and (b) bare gun tube
Close modal

The numerical and tested results of the protection effectiveness of the diamond-shaped thermal jacket are listed in Table 2. It reveals that they were in good agreement. On the whole, the above results showed that the finite element models estimated the temperature field, structural deformation, and the protection effectiveness of the diamond-shaped thermal jacket accurately, with small deviation from the respective tested results. It validates the proposed approaches in a reasonable accuracy.

Comparing with the reported most state-of-the-art thermal jackets for gun barrels, the current diamond-shaped thermal jacket made of the certain braided composites reached a relatively satisfactory level concerning the protection effectiveness. Based on our analysis, the proposed design showed a significant improvement over the earlier designs. An earlier design was carried out in house, and the scheme is as follows. The thermal jacket was fabricated from a thin sheet of aluminum into a hollow circular shape. During installation, the inner wall of the thermal jacket was elevated by 3 mm with silicone pads, isolating it from the outer wall of the gun tube. The arrangement ultimately formed an air gap layer. Utilizing the low thermal conductivity of air, the design achieved its purpose of heat insulation. It shows that a protection efficiency of 50% was observed. Comparing with that scheme, the enhancement produced by the current design is primarily due to the advantages of the insulating effect of the air gap layer and the excellent insulation properties of the thermal jacket material itself. The results are expected to assist thermal jacket design work, where the developed methods provide a more comprehensive assessment of thermal protection performance, allowing a thermal jacket to be high in both protection efficiency and structure function. Further simulation models considering the strength of the connection between the thermal jacket and the gun tube structure may help to better understand the characteristics of the coupled thermal–mechanical problem, because there may be failure caused by internal stress, and it will be studied in future work.

Effects of Structural Parameters of Thermal Jackets.

To investigate the effects of structural parameters of thermal jackets, especially the thickness and air gap, a parametric study using previously validated numerical method was conducted. The numerical models of the shrouded gun barrel for different thicknesses from 1 mm to 5 mm, with an increment of 1 mm, were established by keeping the neutral plane of the thermal jacket unchanged, and the simulations were carried out. As indicated earlier, the cross size scale factor of the thermal jacket can be used to study the effects of the air gap between the thermal jacket and gun tube for convenience. The simulations were performed for different cross size scales from 100% to 180%, with an increment of 20%, under the thermal jacket's thickness of 2 mm. Similarly, the same heat flux, ambient temperature, and heat transfer properties were assumed. Figure 9(a) shows the numerical results for the vertical displacement of gun muzzle under different thickness cases of thermal jackets, and Fig. 9(b) shows the results under different cross size scales.

Fig. 9
Numerical vertical displacement of gun muzzle under different structural parameters of thermal jackets: (a) different thickness cases and (b) different cross size scales
Fig. 9
Numerical vertical displacement of gun muzzle under different structural parameters of thermal jackets: (a) different thickness cases and (b) different cross size scales
Close modal

As a whole, it can be found that the muzzle deflection decreased with increasing thermal jacket's thickness. When the thickness increased to be 5 mm, the vertical displacement appeared to be a positive value. Probably it is caused by the coupled thermal–mechanical interaction where the anisotropy properties of thermal expansion have been taken into account, and the negative coefficients of thermal expansion are in certain directions.

Overall, the muzzle deflection decreased with increasing cross size scales. When the cross size scale increased to be 160% and 180%, the vertical displacement tended to be positive values, and the difference was found to be insignificant. It indicates that there is a limit to reducing muzzle deflection only by increasing the air gap size.

Since there are limitations to the shrouded structure in product's casing weight, the original scheme seems to be qualified and acceptable by the calculated data. A potential research direction is to carry out structural parameter optimization research. An adequate design of structural parameters of thermal jackets may lead to appropriately negligible muzzle deflection. Considering the lightweight, under the premise of ensuring structural rigidity and strength, finding structural design parameters of thermal jackets with higher protection efficiency is promising.

Conclusions

This paper presents the experimental and numerical investigations on the protection efficiency of a diamond-shaped thermal jacket for gun barrels. Some conclusions can be drawn from the experimental and computational results.

  1. Experimental data have shown the adequacy of the calculation method and validated the developed models for the study of solar radiation on the thermal characteristics and deformation state of the gun barrels with and without the diamond-shaped thermal jacket.

  2. The temperature changes together with their gradients, as well as the thermal deformation of the gun tube shrouded with the thermal jacket were notably less than that of the bare gun tube. The nonuniform temperature distribution caused by unilateral radiation can be substantially ameliorated through the thermal jacket. The developed diamond-shaped thermal jacket made of the certain braided composites owned satisfactory protection effectiveness.

  3. Moderately increasing the thermal jacket's thickness or the air gap between the thermal jacket and gun tube can decrease the muzzle deflection of the shrouded gun barrels subjected to unilateral thermal radiation. It is limited to reduce muzzle deflection only by increasing the air gap size.

The work is expected to give an insight into thermal–structural behavior of a diamond-shaped thermal jacket made of braided composites with anisotropic material properties, and provide both theoretical and practical contributions in design of shrouded tank gun barrels aiming at achieving high first shot accuracy. Design parameter optimization of thermal jackets to improve their protection efficiency by permissible increase in weight and size, on the premise of ensuring structural rigidity and strength, is contemplated in the near future.

Funding Data

  • National Natural Science Foundation of China (Grant No. 51705253; Funder ID: 10.13039/501100001809).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

References

1.
Han
,
T. H.
,
2006
, “
Analysis of the Effectiveness of Thermal Shroud on the Thermal Deformation of a Gun Barrel
,”
NDIA 41st Annual Armament Systems: Gun and Missile Systems Conference and Exhibition
, Sacramento, CA, Mar. 27–30.
2.
Dursun
,
T.
,
Utlu
,
C.
, and
Ozkan
,
E. N.
,
2018
, “
Effects of Tank Gun Structural Components on the First Shot Hit Probability
,”
Def. Sci. J.
,
68
(
3
), pp.
273
281
.10.14429/dsj.68.12246
3.
Cao
,
W. Y.
,
Zhang
,
W. Z.
, and
Wang
,
D. H.
,
1989
,
High-Pressure Gun Technology
,
National Defence Industry Press
,
Beijing, China
.
4.
Minor
,
T. C.
,
Lynn
,
F. R.
, and
Deas
,
R. W.
,
1976
, “
Rational Design of Thermal Jackets for Tank Guns
,”
Proceedings of the 2nd International Symposium on Ballistics
, Daytona Beach, FL, Mar. 9–11, pp.
1
13
.
5.
Kingsbury
,
H. B.
, and
Kalbag
,
A. V.
,
1989
, “
A Study of the Effects of the Thermal Shield Temperature Changes on Gun Tube Curvature
,” U.S.
Army Ballistic Research Laboratory, Aberdeen Proving Ground
,
MD
, Technical Report No. ADA209551.
6.
Cote
,
P. J.
,
1993
, “
Thermal Expansion, Modulus, and Muzzle Drift
,” U.S. Army ARDEC Benet Laboratories, New York, Technical Report No. ADA265564.
7.
Bundy
,
M.
,
1990
, “
Experimental Methods for Simulating the Thermal Effects of Gun Firing
,” U.S.
Army Ballistic Research Laboratory, Aberdeen Proving Ground
,
MD
, Technical Report No. BRL-MR-3849.
8.
Bundy
,
M.
,
1996
, “
Temperature-Controlled Bending of a Gun Tube
,” U.S.
Army Research Laboratory, Aberdeen Proving Ground
,
MD
, Technical Report No. ARL-MR-315.
9.
Bundy
,
M.
, and
Patton
,
B.
,
1996
, “
Variation in Shot Impacts Due to Controlled Bending of a Gun
,” U.S.
Army Research Laboratory, Aberdeen Proving Ground
,
MD
, Technical Report No. ARL-TR-1190.
10.
Liu
,
B.
, and
Pan
,
H. X.
,
2010
, “
Research on Protection Efficiency Test for Thermal Jacket of Gun Barrel
,”
Acta Armamentarii
,
31
(
8
), pp.
1032
1035
.https://www.researchgate.net/publication/290971917_Research_on_protection_efficiency_test_for_thermal_jacket_of_gun_barrel
11.
Liu
,
B.
, and
Pan
,
H. X.
,
2011
, “
Parameter Adjustment Method for a Test System of the Protective Effect of a Thermal Protection Jacket Based on Binary Particle Swarm Optimization
,”
Mech. Sci. Technol. Aerosp. Eng.
,
30
(
8
), pp.
1280
1284
.
12.
Birulya
,
M. A.
,
2019
, “
Experimental Evaluation of the Effectiveness of a Heat Shield Casing of Composite Material for the Barrel of a Tank Gun
,”
Issues of Defense Technology: Scientific and Technical Journal, Series 16, Technical Means of Countering Terrorism
,
16
(
127–128
), pp.
128
137
.
13.
Gerber
,
N.
, and
Bundy
,
M.
,
1996
, “
Heating of a Tank Gun Barrel: Numerical Study
,” U.S.
Army Research Laboratory, Aberdeen Proving Ground
,
MD
, Technical Report No. ADA241136.
14.
Chen
,
T. C.
,
Liu
,
C. C.
,
Jang
,
H. Y.
, and
Tuan
,
P. C.
,
2007
, “
Inverse Estimation of Heat Flux and Temperature in Multi-Layer Gun Barrel
,”
Int. J. Heat Mass Transfer
,
50
(
11–12
), pp.
2060
2068
.10.1016/j.ijheatmasstransfer.2006.11.022
15.
Degirmenci
,
E.
, and
Dirikolu
,
M. H.
,
2012
, “
A Thermochemical Approach for the Determination of Convection Heat Transfer Coefficients in a Gun Barrel
,”
Appl. Therm. Eng.
,
37
, pp.
275
279
.10.1016/j.applthermaleng.2011.11.029
16.
Wu
,
B.
,
Chen
,
G.
, and
Xia
,
W.
,
2008
, “
Heat Transfer in a 155 mm Compound Gun Barrel With Full Length Integral Midwall Cooling Channels
,”
Appl. Therm. Eng.
,
28
(
8–9
), pp.
881
888
.10.1016/j.applthermaleng.2007.07.010
17.
Liu
,
M. S.
,
Dong
,
Q. W.
,
Wang
,
D. B.
, and
Ling
,
X.
,
1999
, “
Numerical Simulation of Thermal Stress in Tube-Sheet of Heat Transfer Equipment
,”
Int. J. Pressure Vessels Pip
ing,
76
(
10
), pp.
671
675
.10.1016/S0308-0161(99)00037-X
18.
Islamoglu
,
Y.
,
2004
, “
Numerical Analysis of the Influence of a Circular Fin With Different Profiles on the Thermal Characteristics in a Ceramic Tube of Heat Transfer Equipment
,”
Int. J. Pressure Vessels Pip
ing,
81
(
7
), pp.
583
587
.10.1016/j.ijpvp.2004.04.009
19.
Peng
,
X. L.
, and
Li
,
X. F.
,
2010
, “
Thermoelastic Analysis of a Cylindrical Vessel of Functionally Graded Materials
,”
Int. J. Pressure Vessels Pip
ing,
87
(
5
), pp.
203
210
.10.1016/j.ijpvp.2010.03.024
20.
Ahn
,
S. T.
,
2007
, “
An Analytical and Experimental Study on the Thermal Shroud Effect to Minimize Thermal Deformation of a High L/D Ratio Cylinder
,”
J. Fluid Mach.
,
10
, pp.
54
63
.10.5293/KFMA.2007.10.5.054
21.
Bogomolov
,
P. I.
,
Kozlov
,
I. A.
, and
Korenev
,
P. A.
,
2017
, “
Numerical and Experimental Investigation of Solar Radiation on the Guide Tube With a Heat-Protective Housing
,”
Tech.-Technol. Probl. Serv.
,
39
(
1
), pp.
9
13
.
22.
Han
,
D.
,
2021
, “
Winding Technology of Spiral Sheath Research on Thermoforming Technology Advance and Automatic
,” Master's thesis,
North University of China
,
Taiyuan, China
.
23.
Dong
,
K.
,
Zhang
,
J.
,
Jin
,
L.
,
Gu
,
B.
, and
Sun
,
B.
,
2016
, “
Multi-Scale Finite Element Analyses on the Thermal Conductive Behaviors of 3D Braided Composites
,”
Compos. Struct.
,
143
, pp.
9
22
.10.1016/j.compstruct.2016.02.029
24.
Lundström
,
F.
,
Frogner
,
K.
, and
Andersson
,
M.
,
2021
, “
Analysis of the Temperature Distribution in Weave-Based CFRP During Induction Heating Using a Simplified Numerical Model With a Cross-Ply Representation
,”
Composites, Part B
,
223
, p.
109153
.10.1016/j.compositesb.2021.109153
25.
Bower
,
A. F.
,
2010
,
Applied Mechanics of Solids
, 1st ed.,
CRC Press
,
Boca Raton, FL
.
26.
Hull
,
D.
, and
Clyne
,
T. W.
,
1996
,
An Introduction to Composite Materials
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.
27.
Ning
,
Z.
,
Liu
,
R.
,
Elhajjar
,
R. F.
, and
Wang
,
F.
,
2017
, “
Micro-Modeling of Thermal Properties in Carbon Fibers Reinforced Polymer Composites With Fiber Breaks or Delamination
,”
Composites, Part B
,
114
, pp.
247
255
.10.1016/j.compositesb.2017.01.036
28.
Wu
,
Y. H.
,
2013
, “
Analysis of the Temperature Field of a Gun Tube Based on Thermal-Solid Coupling
,”
Res. J. Appl. Sci., Eng. Technol.
,
5
(
16
), pp.
4110
4117
.10.19026/rjaset.5.4634
29.
Luo
,
L. K.
, and
Zhu
,
Y. G.
,
2010
, “
Influence of the Temperature Field of Tank Gun Barrel on Firing Accuracy
,”
Fire Control Command Control
,
35
(
3
), pp.
75
77
.